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DOE OSTI2022

Condition monitoring and anomaly detection in cyber-physical systems

The modern industrial environment is equipping myriads of smart manufacturing machines where the state of each device can be monitored continuously. Such monitoring can help identify possible future failures and develop a cost-effective maintenance plan. However, it is a daunting task to perform early detection with low false positives and negatives from the huge volume of collected data. This requires developing a holistic machine learning framework to address the issues in condition monitoring of high priority components and develop efficient techniques to detect anomalies that can detect and possibly localize the faulty components. This paper presents a comparative analysis of recent machine learning approaches for robust, cost-effective anomaly detection in cyber-physical systems. While detection has been extensively studied, very few researchers have analyzed the localization of the anomalies. We show that supervised learning outperforms unsupervised algorithms. For supervised cases, we achieve near-perfect accuracy of 98% (specifically for tree-based algorithms). In contrast, the best-case accuracy in the unsupervised cases was 63%—the area under the receiver operating characteristic curve (AUC) exhibits similar outcomes as an additional metric.

Marfo, William↗

DOE OSTI2022

Cosmogenic 10Be constraints on deglacial snowline rise in the Southern Alps, New Zealand

We report geochronological dating of glacial landforms, such as terminal and lateral moraines, is useful for determining the extent and timing of past glaciation and for reconstructing the magnitude and rate of past climate changes. In the Southern Alps of New Zealand, well-dated glacial geomorphological records constrain the last glacial cycle across much of the Waitaki River basin (e.g. Ōhau, Pukaki, Tekapo) but its southern sector such as the Ahuriri River valley remains comparatively unconstrained. Recently, there has been debate on the scale and rapidity of mountain glacier retreat during the last glacial termination, particularly the 20–17 ka period in New Zealand. Missing from this debate is well-constrained equilibrium-line altitude (ELA) and associated temperature reconstructions, particularly over the period around 17 ka, which can help us to develop a more complete picture of how past temperature changes drove glacier retreat. Here we report the first glacial chronology dataset from the Last Glacial Maximum (LGM) and subsequent deglaciation from the Ahuriri River valley, Southern Alps, New Zealand (44°23'54"S, 169°39'48"E) based on 38 beryllium-10 ( 10 Be) surface-exposure ages from terminal moraine systems and glaciated bedrock situated at the lower and middle sections of the valley. Our results show that the former Ahuriri Glacier reached its maximum extent at 19.8 ± 0.3 ka, which coincides with the global Last Glacial Maximum. By 16.7 ± 0.3 ka, the glacier had retreat ~18 km up-valley suggesting at least ~43% glacier-length loss relative to its full LGM extent. This deglaciation was accompanied by the formation of a shallow proglacial lake. Using the accumulation area ratio (AAR) method, we estimate that the ELA was lower than present by ~880 m (~1120 m a.s.l.) at 19.8 ± 0.3 ka, and ~770 m lower (~1230 m a.s.l.) at 16.7 ± 0.3 ka. Applying an estimate for temperature lapse rate, this ELA anomaly implies that local air temperature was 5 ± 1 °C colder than present (1981–2010) at 19.8 ± 0.3 ka, while it was 4.4 ± 0.9 °C colder at 16.7 ± 0.3 ka, assuming no change in precipitation. The substantial glacier retreat in response to a relatively small accompanying increases in ELA (110 m) and temperature (0.6 °C) may have been a result of the high glacier-length sensitivity of this glacier system due to its low gradient of former ice surface. Our low warming estimate differs markedly from other deglaciation studies, specifically from Rakaia River valley, which reports a much larger temperature increase at the onset of the last deglaciation. This precisely-dated moraine record along with reconstructed ELA as proxies for atmospheric conditions, provides new insight into post LGM glacier behaviour and climate conditions in New Zealand.

58 GEOSCIENCES↗

DOE OSTI2023

Searching for Novel Chemistry in Exoplanetary Atmospheres Using Machine Learning for Anomaly Detection

Abstract The next generation of telescopes will yield a substantial increase in the availability of high-quality spectroscopic data for thousands of exoplanets. The sheer volume of data and number of planets to be analyzed greatly motivate the development of new, fast, and efficient methods for flagging interesting planets for reobservation and detailed analysis. We advocate the application of machine learning (ML) techniques for anomaly (novelty) detection to exoplanet transit spectra, with the goal of identifying planets with unusual chemical composition and even searching for unknown biosignatures. We successfully demonstrate the feasibility of two popular anomaly detection methods (local outlier factor and one-class support vector machine) on a large public database of synthetic spectra. We consider several test cases, each with different levels of instrumental noise. In each case, we use receiver operating characteristic curves to quantify and compare the performance of the two ML techniques.

Astronomy & Astrophysics↗

DOE OSTI2025

Research in Theoretical Particle Physics: Neutrino Masses and The Origin of CP-Violation

The main goal of this project was to investigate the theories of neutrino masses at the low scale and the origin of CP-violation in physics beyond the Standard Model. The origin of neutrino masses is one of the most pressing issues in particle physics. In this proposal, we investigated the theories for neutrino masses based on local total lepton number. In these theories anomaly cancellation predicts the existence of extra fermions with lepton number, and one of them is a good dark matter (DM) candidate. The cosmological constraints on the DM relic density implies that the lepton number symmetry breaking scale must be below the multi-TeV scale. Therefore, one can hope to test the origin of neutrino masses in current or future experiments. We investigated in great detail the anomaly cancellation in these gauge theories, study the different mechanisms for neutrino masses, study the predictions for direct and indirect dark matter experiments. Since these theories predict new sources of CP violation, we investigated the predictions for the electric dipole moments (EDM). The Higgs decays and the different signatures at the Large Hadron Collider were investigated in great detail. Finally, we studied the possible baryogenesis mechanisms in these theories in agreement with the EDM, DM and collider constraints. The origin of CP violation in the Standard Model is unknown. In this proposal, we investigated the simplest mechanisms for spontaneous CP-violation to explain the CP-violation in the CKM matrix and the value of the QCD vacuum angle. We discussed the Nelson-Barr mechanism in gauge theories predicting vector-like quarks from anomaly cancellation such as theories for local baryon number. We discussed the Bento-Branco-Parada mechanism in gauge theories to explain the CP-Violation in the CKM matrix. We will investigate models with two Higgs doublets in the context of the minimal theory for quark-lepton unification. We will show the non-decoupling effects in the Higgs sector, the main constraints coming from flavour violating processes when the Yukawa couplings are related by the gauge symmetry in theories for quark-lepton unification. We will investigate the predictions for electric dipole moments in these theories. The possibility to have successful baryogenesis was investigated. Finally, we investigated the relation between CP-violation in the quark and leptonic sectors. The future results from these studies could help us to understand two main issues in physics beyond the Standard Model: The Origin of Neutrino Masses and CP-violation.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2020

Anomaly Detection and Mitigation for Wide-Area Damping Control using Machine Learning

In an interconnected multi-area power system, wide-area measurement based damping controllers are used to damp out inter-area oscillations, which jeopardize grid stability and constrain the power flows below to their transmission capacity. The effect of wide-area damping control (WADC) significantly depends on both power and cyber systems. At the cyber system layer, an adversary can inflict the WADC process by compromising either measurement signals, control signals or both. Stealthy and coordinated cyber-attacks may bypass the conventional cybersecurity measures to disrupt the seamless operation of WADC. This paper proposes an anomaly detection (AD) algorithm using supervised Machine Learning and a model-based logic for mitigation. The proposed AD algorithm considers measurement signals (input of WADC) and control signals (output of WADC) as input to evaluate the type of activity such as normal, perturbation (small or large signal faults), attack and perturbation-and-attack. Upon anomaly detection, the mitigation module tunes the WADC signal and sets the control status mode as either wide-area mode or local mode. The proposed anomaly detection and mitigation (ADM) module works inline with the WADC at the control center for attack detection on both measurement and control signals and eliminates the need for ADMs at the geographically distributed actuators. Here, we consider coordinated and primitive data-integrity attack vectors such as pulse, ramp, relay-trip and replay attacks. The performance of the proposed ADM algorithms was evaluated under these attack vector scenarios on a testbed environment for 2-area 4-machine power system. The ADM module shows effective performance with 96:5% accuracy to detect anomalies.

22 GENERAL STUDIES OF NUCLEAR REACTORS↗

DOE OSTI2021

Removing the Effects of Tropical Dynamics from North Pacific Climate Variability

Teleconnections from the Tropics energize variations of the North Pacific climate, but detailed diagnosis of this relationship has proven difficult. Simple univariate methods, such as regression on El Niño-Southern Oscillation (ENSO) indices, may be inadequate since the key dynamical processes involved -- including ENSO diversity in the Tropics, re-emergence of mixed layer thermal anomalies, and oceanic Rossby wave propagation in the North Pacific -- have a variety of overlapping spatial and temporal scales. Here we use a multivariate Linear Inverse Model to quantify tropical and extra-tropical multi-scale dynamical contributions to North Pacific variability, in both observations and CMIP6 models. In observations, we find that the Tropics are responsible for almost half of the seasonal variance, and almost three quarters of the decadal variance, along the North American coast and within the subtropical front region northwest of Hawaii. SST anomalies that are generated by local dynamics within the Northeast Pacific have much shorter time scales, consistent with transient weather forcing by Aleutian low anomalies. Variability within the Kuroshio-Oyashio Extension (KOE) region is considerably less impacted by the Tropics, on all time scales. Consequently, without tropical forcing the dominant pattern of North Pacific variability would be a KOE pattern, rather than the Pacific Decadal Oscillation (PDO). In contrast to observations, most CMIP6 historical simulations produce North Pacific variability that maximizes in the KOE region, with amplitude significantly higher than observed. Correspondingly, the simulated North Pacific in all CMIP6 models is shown to be relatively insensitive to the Tropics, with a dominant spatial pattern generally resembling the KOE pattern, not the PDO.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Local-thermal-gradient and large-scale-circulation impacts on turbine-height wind speed forecasting over the Columbia River Basin

Abstract. We investigate the sensitivity of turbine-height wind speed forecast to initial condition (IC) uncertainties over the Columbia River Gorge (CRG) and Columbia River Basin (CRB) for two typical weather phenomena, i.e., local-thermal-gradient-induced marine air intrusion and a cold frontal passage. Four types of turbine-height wind forecast anomalies and their associated IC uncertainties related to local thermal gradients and large-scale circulations are identified using the self-organizing map (SOM) technique. The four SOM types are categorized into two patterns, each accounting for half of the ensemble members. The first pattern corresponds to IC uncertainties that alter the wind forecast through a modulating weather system, which produces the strongest wind anomalies in the CRG and CRB. In the second pattern, the moderate uncertainties in local thermal gradient and large-scale circulation jointly contribute to wind forecast anomaly. We analyze the cross section of wind and temperature anomalies through the gorge to explore the evolution of vertical features of each SOM type. The turbine-height wind anomalies induced by large-scale IC uncertainties are more concentrated near the front. In contrast, turbine-height wind anomalies induced by the local IC thermal uncertainties are found above the surface thermal anomalies. Moreover, the wind forecast accuracy in the CRG and CRB is limited by IC uncertainties in a few specific regions, e.g., the 2 m temperature within the basin and large-scale circulation over the northeast Pacific around 140∘ W.

17 WIND ENERGY↗

DOE OSTI2022

WISP: Watching grid Infrastructure Stealthily through Proxies (Final Technical Report)

The complex interdependencies of cyber systems (sensors and communications), physical grids and associated electricity market operations make protecting electric power grids a significant challenge. The energy sector is constantly under new, targeted, advanced and dangerous cyber-attacks that have the potential to result in the loss of human life. These threats are further exacerbated by our need to modernize the grid. One focus of cyber security research in smart grids is the securing of the SCADA system through advanced intrusion detection systems (IDS) and bad data detection algorithms in state estimation. These methods either require full knowledge of the system topology and parameters or fail to understand the physical behaviors under attack. WISP (Watching grid Infrastructure Stealthily through Proxies) is designed to provide additional protection to the power grid using only publicly available data. In particular, WISP exploits the spatio-temporal nature of the real time locational marginal prices (LMPs), in conjunction with other information such as bids, weather, outages and load data to analyze anomalous power pricing behaviors and then correlate those observations to localize regions of interest and identify potential cyber events. WISP is non-intrusive as the tool is deployed as a service in the Cloud or on premise and provides reliable information to system operators for enhanced situational awareness, without impeding energy delivery functions. The WISP technology comprises three modules: the data-driven anomaly detection core, the vulnerability and risk analysis and the root cause analysis. The data-driven anomaly detection core performs the tasks of feature selection, anomaly detection and attack region localization. The vulnerability and risk analysis module provides system level information of the vulnerable variables and times, assisting the operators in selecting monitoring and protection nodes. The root cause analysis module takes the detection results and identifies potential operational conditions that contribute to the detected anomalies. In Phase I, we have demonstrated the feasibility and effectiveness of WISP. We developed a realistic electricity market simulator capable of generating normal and attack market data under various operational conditions. We developed a series of cyber-attack detection and analysis algorithms and evaluated them under multiple data sources. Finally, we integrated all modules into an end-to-end software, providing functions for data management, data analytics and visualization. Specifically, we have achieved: (i) real-time data acceptance from external utility interfaces with >99% acceptance rate; (ii) high performance anomaly detection algorithms with >98% detection accuracy and <0.1% false alarm rate; and (iii) ultra-low computing delay <50 milliseconds. Additionally, our team developed algorithms to identify the vulnerable variables in electricity market operations and root cause analysis functions to identify major contributors to the price spikes. These ancillary modules are necessary when deploying WISP in real world industry environment. In Phase II, we have demonstrated the effectiveness of WISP software on realistic largescale power systems. We performed red team testing for the Phase I WISP software and identified software vulnerabilities and implemented corresponding mitigation solutions. We adapted the electricity market simulator for the Texas synthetic 2000-bus system and generated datasets for the false data injection attacks. We created database and visualization interfaces for the Texas system and the ISO New England system. We performed software optimization in terms of operation efficiency, computing speed and detection accuracy. Finally, we tested the software on the Texas system and the ISO New England system and evaluated the detection performance. Overall, we achieved above 89% detection rate, below 3% false alarm rate and below 37 seconds of end-to-end detection delay.

24 POWER TRANSMISSION AND DISTRIBUTION↗

DOE OSTI2021

Anomalous Behavior in the Atomic Structure of Nb$^{3}$Sn under High Pressure

In the present study, the local atomic structure of a Nb3Sn superconductor sample has been probed by X-ray absorption fine structure (XAFS) as a function of hydrostatic pressure (from ambient up to 26 GPa) using a diamond anvil cell set-up. The analysis of the Nb-K edge extended X-ray absorption fine structure (EXAFS) data was carried out combining standard multi shell structural refinement and reverse Monte Carlo method to provide detailed in situ characterization of the pressure-induced evolution of the Nb local structure in Nb3Sn. The results highlight a complex evolution of Nb chains at the local atomic scale, with a peculiar correlated displacement of Nb–Nb and Nb–Nb–Nb configurations. Such a local effect appears related to anomalies evidenced by X-ray diffraction in other superconductors belonging to the same A15 crystallographic structure.

36 MATERIALS SCIENCE↗

DOE OSTI2023

Exactly solvable lattice Hamiltonians and gravitational anomalies

We construct infinitely many new exactly solvable local commuting projector lattice Hamiltonian models for general bosonic beyond group cohomology invertible topological phases of order two and four in any spacetime dimensions, whose boundaries are characterized by gravitational anomalies. Examples include the beyond group cohomology invertible phase without symmetry in (4+1)D that has an anomalous boundary \mathbb{Z}_2 ℤ 2 topological order with fermionic particle and fermionic loop excitations that have mutual \pi π statistics. We argue that this construction gives a new non-trivial quantum cellular automaton (QCA) in (4+1)D of order two. We also present an explicit construction of gapped symmetric boundary state for the bosonic beyond group cohomology invertible phase with unitary \mathbb{Z}_2 ℤ 2 symmetry in (4+1)D. We discuss new quantum phase transitions protected by different invertible phases across the transitions.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2021

Progress in Epitaxial Thin-Film Na 3 Bi as a Topological Electronic Material

Trisodium bismuthide (Na 3 Bi) is the first experimentally verified topological Dirac semimetal, and is a 3D analogue of graphene hosting relativistic Dirac fermions. Its unconventional momentum-energy relationship is interesting from a fundamental perspective, yielding exciting physical properties such as chiral charge carriers, the chiral anomaly, and weak anti-localization. It also shows promise for realizing topological electronic devices such as topological transistors. Herein, an overview of the substantial progress achieved in the last few years on Na 3 Bi is presented, with a focus on technologically relevant large-area thin films synthesized via molecular beam epitaxy. Key theoretical aspects underpinning the unique electronic properties of Na 3 Bi are introduced. Next, the growth process on different substrates is reviewed. Spectroscopic and microscopic features are illustrated, and an analysis of semiclassical and quantum transport phenomena in different doping regimes is provided. Furthermore, the emergent properties arising from confinement in two dimensions, including thickness-dependent and electric-field-driven topological phase transitions, are addressed, with an outlook toward current challenges and expected future progress.

36 MATERIALS SCIENCE↗

DOE OSTI2024

Impossible symmetries and conformal gravity

We explore the physics of relativistic gapless phases defined by a mixed anomaly between two generalized conserved currents. The gapless modes can be understood as Goldstone modes arising from the nonlinear realization of (generically higher-form) symmetries arising from these currents. In some cases, the anomaly cannot be reproduced by any local and unitary theory, indicating that the corresponding symmetries are impossible, in the sense that they cannot appear in a Lorentzian physical system. We give a general construction and illustrate it with several examples. Most notably, we study conformal gravity from this perspective, describing the higher-form symmetries of the linear theory and showing how it can be understood in terms of anomalies. Along the way we clarify some aspects of electric-magnetic duality in linear conformal gravity.

79 ASTRONOMY AND ASTROPHYSICS↗

DOE OSTI2023

Spread Spectrum Time Domain Reflectometry (SSTDR) and Frequency Domain Reflectometry (FDR) for Detection of Cable Anomalies Using Machine Learning

Cables are initially qualified for nuclear power plant use for 40 years. As plants extend their operating license to 60 and 80 years, continued use of these cables must shift to a performance-based approach since it is cost prohibitive to completely replace cables that are likely still capable of performing their design function. A variety of cable tests are available and are commonly applied during outages when the cables can be taken out of service. Frequency domain reflectometry (FDR) is one of these test methods that is being more broadly accepted and used because it not only detects anomalies along the cable with a low-voltage signal that does not stress the cable insulation, but the technique also locates the anomalies. This supports follow-up local inspection and local repair or partial replacement of a damaged cable segment. Currently, FDR testing is only applied to cables that are taken out of service since the test instrument would be damaged by operational voltages. A related technology that has found some acceptance in the aircraft and rail industry is spread spectrum time domain reflectometry (SSTDR). This technology has been implemented with a custom commercial instrument by LiveWire Innovation Inc. that is designed to operate on live cables up to 1000 volts. One of the main conclusions of a previous effort was that cable reflectometry plots can be difficult for humans to analyze due to baseline noise, low or noisy anomaly response peaks, or large responses from cable ends. Detection of cable anomalies for many of these frequencies and test conditions was challenging for manual analysis. This presented an ideal opportunity for ML analysis to distinguish undamaged cable indications from anomalous cable indications. This research discusses application of machine learning (ML) to reflectometry cable test methods. The goal was to assess feasibility to distinguish undamaged cable reflectometry responses from damaged or anomalous cable reflectometry responses. The assessment considered the 3 instruments, multiple frequency bandwidths from each instrument, multiple cable anomalies and test conditions, and both supervised and unsupervised ML approaches. Although approaches and analysis methods were not identical or directly comparable, both outputs were encouraging. The unsupervised prediction weighted accuracy was assessed by instrument and by frequency. It performed better at high frequencies with the highest prediction accuracy of 0.84 for the higher frequency FDR, 0.79 for the 48-MHz LiveWire SSTDR, and 0.77 for 300-MHz PNNL SSTDR. The initial weighted accuracy average across all frequencies for using supervised ML was 0.56 to 0.68. The supervised analysis was repeated with noisier training data removed resulting in weighted accuracies of 0.69 to 0.87. These weighted accuracies are not directly comparable due to differences in the supervised and unsupervised analysis details but do indicate an encouraging trend. Even with limited and unbalanced data, strong prediction accuracies seem encouraging for further work including more data under a wider range of conditions.

42 ENGINEERING↗

DOE OSTI2024

SSTDR and FDR Detection of Un-Energized and Energized Cable Anomalies Including Thermal Degradation Using Machine Learning

Historically, cables are initially qualified for nuclear power plant use for 40 years. As plants extend their operating license to 60 and 80 years, continued use of these cables must shift to a performance-based approach since it is cost prohibitive to completely replace cables that are likely still capable of performing their design function. A variety of cable tests are available and are commonly applied during outages when the cables can be taken out of service. Frequency domain reflectometry (FDR) is one of these test methods that is being more broadly accepted and used because it not only detects anomalies along the cable with a low-voltage signal that does not stress the cable insulation, but the technique also locates the anomalies. This supports follow-up local inspection and local repair or partial replacement of a damaged cable segment. Currently, FDR testing is only applied to cables that are taken out of service since the test instrument would be damaged by operational voltages. A related technology that has found some acceptance in the aircraft and rail industry is spread spectrum time domain reflectometry (SSTDR). This technology has been implemented with a custom commercial instrument by LiveWire Innovation that is designed to operate on live cables up to 1000 volts and with a bandwidth of 48 MHz. Initial evaluation by the Pacific Northwest National Laboratory (PNNL) of the Live Wire system indicated that a broader bandwidth (BW) SSTDR may be better for many kinds of flaws. This led PNNL to develop an SSTDR laboratory instrument suitable for tests up to 500 MHz bandwidth. Testing on energized cables is also desirable for online monitoring systems so an inductive clamshell coupler was developed that allows energized cables to be tested up to at least 5 kV and likely higher voltage levels. Dielectric spectroscopy and tan delta testing plus various laboratory destructive tests were included in this data acquisition campaign directed to feed a machine learning (ML) study. With these kinds of developments, online energized cable tests may be possible with industrial adoption of such hardware advances but it will be completely impractical to have highly skilled data analysts continually examine these complex signals for indications of damage or compromised conditions. If online testing is to be implemented in new test hardware, it must be accompanied by software that can interpret the signals and alert plant operators of changing or degraded conditions. The thermally aged, shielded cable investigated here was separately treated for ML analysis. Visual analysis of electrical data showed generally increasing peaks where the cable entered and exited the oven. These peaks were not exactly aligned with expected locations, but these differences were attributed to velocity of propagation calibration errors. Only supervised ML was applied to the thermally aged data as this data was only available shortly before the committed publication date of this report. The supervised ML was structured to divide the 0 to 70-day responses as ‘normal’ from 0 to 35 days or ‘anomalous’ from 36 to 70 days, based on cable tensile elongation at break (EAB) insulation characterization. Using 80% of the data for training and 20% for testing, the supervised ML predicted normal versus anomalous was 70% accurate. Important conclusions include: • Accuracy to predict the presence of cable damage is improved from the 2023 effort by more training data. Weighted accuracies for comparisons among the instruments ranged from 67 to 89 % for unsupervised ML and 71 to 99% for supervised ML. • Based on the synthetic data tests, the unsupervised models are more generalizable to unseen anomalies. The Multi-Layer Perceptron classifier (MLP) model reported as high as 99.7% accuracy on the test data, but this dropped to 58.3% when tested on the synthetic data. In contrast, the unsupervised Pointwise model only achieved 89.7% accuracy on the experimental data but reported 78.3% accuracy on the synthetic data. • The best anomaly indicators are higher frequency (400 MHz BW) FDR data. Other tests may be interesting but for this study, this was the best predicter.

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2023

Spread Spectrum Time Domain Reflectometry (SSTDR) and Frequency Domain Reflectometry (FDR) for Detection of Cable Anomalies Using Machine Learning

46 INSTRUMENTATION RELATED TO NUCLEAR SCIENCE AND ↗

DOE OSTI2024

SSTDR and FDR Detection of Un-Energized and Energized Cable Anomalies Including Thermal Degradation Using Machine Learning

36 MATERIALS SCIENCE↗

DOE OSTI2021

Anomaly-induced edge currents in hydrodynamics with parity anomaly

Here in this paper, we discuss relativistic hydrodynamics for a massless Dirac fermion in (2 + 1) dimensions, which has the parity anomaly—a global ’t Hooft anomaly between U(1) and parity symmetries. We investigate how hydrodynamics implements the party anomaly, particularly focusing on the transport phenomena at the boundary. Based on the parity anomaly matching and the second law of local thermodynamics, we find U(1) and entropy currents localized at the boundary, as well as the bulk anomalous current with vanishing divergence. These edge currents are similar to the ( 1 + 1)-dimensional chiral transports, but the coefficients are given by half of theirs. We also generalize our discussion to more general anomalies among multiple U(1) symmetries and single $\mathbb{Z}_2$ symmetry.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2021

On exotic consistent anomalies in (1+1)$d$: A ghost story

We revisit ’t Hooft anomalies in (1+1) d d non-spin quantum field theory, starting from the consistency and locality conditions, and find that consistent U(1) and gravitational anomalies cannot always be canceled by properly quantized (2+1) d d classical Chern-Simons actions. On the one hand, we prove that certain exotic anomalies can only be realized by non-reflection-positive or non-compact theories; on the other hand, without insisting on reflection-positivity, the exotic anomalies present a caveat to the inflow paradigm. For the mixed U(1) gravitational anomaly, we propose an inflow mechanism involving a mixed U(1) \times × SO(2) classical Chern-Simons action with a boundary condition that matches the SO(2) gauge field with the (1+1) d d spin connection. Furthermore, we show that this mixed anomaly gives rise to an isotopy anomaly of U(1) topological defect lines. The isotopy anomaly can be canceled by an extrinsic curvature improvement term, but at the cost of creating a periodicity anomaly. We survey the holomorphic bc b c ghost system which realizes all the exotic consistent anomalies, and end with comments on a subtlety regarding the anomalies of finite subgroups of U(1).

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗