Chiral waves on the Fermi-Dirac sea: Quantum superfluidity and the axial anomaly
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73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
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Charge-dependent flow induced by electromagnetic fields in heavy ion collisions
The colliding heavy ions create extremely strong magnetic and electric fields that significantly affect the evolution of the produced quark-gluon plasma (QGP). The knowledge of these fields is essential for establishing the role of topological fluctuations in the QGP through the chiral magnetic effect and related anomaly-induced phenomena. In this talk, we describe our work on the evolution of the QGP in electric and magnetic fields in the framework of hydrodynamics supplemented, in a perturbative fashion, by the dynamical electromagnetism. The evolution of the QGP fluid is described within the iEBE-VISHNU framework. We find that the electromagnetically induced currents result in a charge-odd directed flow Δv 1 and a charge-odd Δv 3 flow both of which are odd in rapidity. Furthermore, while the predicted magnitude of these charge-odd flows agrees with the data from RHIC and LHC, the sign of the predicted asymmetry between the flows of positive and negative hadrons is opposite to the data.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Generalized Ginsparg-Wilson relations
We give a general derivation of Ginsparg-Wilson relations for both Dirac and Majorana fermions in any dimension. These relations encode continuous and discrete chiral, parity and time-reversal anomalies and will apply to the various classes of free-fermion topological insulators and superconductors (in the framework of a relativistic quantum field theory in Euclidean spacetime). We show how to formulate the exact symmetries of the lattice action and the relevant index theorems for the anomalies. Published by the American Physical Society 2024
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Wave-function-based emulation for nucleon-nucleon scattering in momentum space
Emulators for low-energy nuclear physics can provide fast and accurate predictions of bound-state and scattering observables for applications that require repeated calculations with different parameters, such as Bayesian uncertainty quantification. In this paper, we extend a scattering emulator based on the Kohn variational principle (KVP) to momentum space (including coupled channels) with arbitrary boundary conditions, which enable the mitigation of spurious singularities known as Kohn anomalies. We test it on a modern chiral nucleon-nucleon (N N) interaction, including emulation of the coupled channels. We provide comparisons between a Lippmann-Schwinger equation emulator and our KVP momentum-space emulator for a representative set of neutron-proton (n p) scattering observables, and also introduce a quasi-spline-based approach for the KVP-based emulator. Furthermore, our findings show that while there are some trade-offs between accuracy and speed, all three emulators perform well. Self-contained Jupyter notebooks that generate the results and figures in this paper are publicly available.
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Spin Sum Rule of the Nucleon in the QCD Instanton Vacuum
We briefly review some essential aspects of the QCD instanton vacuum in relation to the quantum breaking of conformal symmetry, the spontaneous breaking of chiral symmetry, and the axial U(1) anomaly. The anomaly causes the intrinsic nucleon spin to transmute to the vacuum topological charge by quantum tunneling. We use Ji′s invariant spin decomposition to discuss the spin budget of the nucleon as a quark–diquark state in the QCD instanton vacuum. A measure of the intrinsic quark spin of the nucleon is a measure of the quenched topological susceptibility of the QCD instanton vacuum.
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
Standard model and the lattice
The S U ( 3 ) ⊗ S U ( 2 ) ⊗ U ( 1 ) standard model maps smoothly onto a conventional lattice gauge formulation, including the parity violation of the weak interactions. The formulation makes use of the pseudoreality of the weak group and requires the inclusion a full generation of both leptons and quarks. As in continuum discussions, chiral eigenstates of the Dirac operator generate known anomalies, although with rough gauge configurations these are no longer exact zero modes of the Dirac operator. Published by the American Physical Society 2024
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Generalized Ginsparg-Wilson relations: Fermionic anomalies on the lattice
The Ginsparg-Wilson (GW) relation elegantly captures how the anomalous chiral symmetry of a Dirac fermion manifests on the lattice. In this talk, we discuss how the GW relation and its closed-form solution, the overlap operator, can be generalized to Majorana or Dirac fermions in any dimension for finite symmetry transformations (continuous or discrete). We find an exact symmetry which reproduces both perturbative and global anomalies on the lattice. These generalized GW fermions are boundary theories of various bulk symmetry-protected topological phases and thus provide an explicit lattice realization of the fermionic bulk-boundary correspondence central to recent proposals for chiral gauge theories on the lattice.
Singh, Hersh [Fermilab] (ORCID:0000000220026959)↗
Flavor-violating ALPs, electron g − 2 , and the Electron-Ion Collider
We revisit the possibility that light axionlike particles (ALPs) with lepton-flavor-violating couplings could give significant contributions to the electron’s anomalous magnetic moment g e − 2 . Unlike flavor diagonal lepton-ALP couplings, which are exclusively axial, lepton-flavor-violating couplings can have arbitrary chirality. Focusing on the e − τ ALP coupling, we find that the size of the contribution to g e − 2 depends strongly on the chirality of the coupling. A significant part of the parameter space for which such a coupling can explain experimental anomalies in g e − 2 can be probed at the Electron-Ion Collider, which is uniquely sensitive to the chirality of the coupling using the polarization of the electron beam. Published by the American Physical Society 2024
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Trace anomaly form factors from lattice QCD
The hadron mass can be obtained through the calculation of the trace of the energy-momentum tensor in the hadron which includes the trace anomaly and sigma terms. The anomaly due to conformal symmetry breaking is believed to be an important ingredient for hadron mass generation and confinement. In this work, we will present the calculation of the glue part of the trace anomaly form factors of the pion up to Q 2 ∼ 4.3 GeV 2 and the nucleon up to Q 2 ∼ 1 GeV 2 . The calculations are performed on a domain wall fermion ensemble with overlap valence quarks at seven valence pion masses varying from ∼ 250 to ∼ 540 MeV , including the unitary point ∼ 340 MeV . We calculate the radius of the glue trace anomaly for the pion and the nucleon from the z expansion. By performing a two-dimensional Fourier transform on the glue trace anomaly form factors in the infinite momentum frame with no energy transfer, we also obtain their spatial distributions for several valence quark masses. The results are qualitatively extrapolated to the physical valence pion mass with systematic errors from the unphysical sea quark mass, discretization effects in the renormalization sum rule, and finite-volume effects to be addressed in the future. We find the pion’s form factor changes sign, as does its spatial distribution, for light quark masses. This explains how the trace anomaly contribution to the pion mass approaches zero toward the chiral limit. Published by the American Physical Society 2024
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Nonlocal Effective Field Theory and Its Applications
We review recent applications of nonlocal effective field theory, particularly focusing on nonlocal chiral effective theory and nonlocal quantum electrodynamics (QED), as well as an extension of nonlocal effective theory to curved spacetime. For the chiral effective theory, we discuss the calculation of generalized parton distributions (GPDs) of the nucleon at nonzero skewness, along with the corresponding gravitational (or mechanical) form factors, within the convolution framework. In the QED application, we extend the nonlocal formulation to construct the most general nonlocal QED interaction, in which both the propagator and fundamental QED vertex are modified due to the nonlocal Lagrangian, while preserving the Ward–Green–Takahashi identities. For consistency with the modified propagator, a solid quantization is proposed, and the nonlocal QED is applied to explain the lepton g−2 anomalies without the introduction of new particles beyond the standard model. Finally, with an extension of the chiral effective action to curved spacetime, we investigate the nonlocal energy–momentum tensor and gravitational form factors of the nucleon with a nonlocal pion–nucleon interaction.
chiral effective field theory↗
Upper limit on the chiral magnetic effect in isobar collisions at the Relativistic Heavy-Ion Collider
The chiral magnetic effect (CME) is a phenomenon that arises from the QCD anomaly in the presence of an external magnetic field. The experimental search for its evidence has been one of the key goals of the physics program of the Relativistic Heavy-Ion Collider. The STAR Collaboration has previously presented the results of a blind analysis of isobar collisions ( Ru 44 96 + Ru 44 96 , Zr 40 96 + Zr 40 96 ) in the search for the CME. The isobar ratio ( Y ) of CME-sensitive observable, charge separation scaled by elliptic anisotropy, is close to but systematically larger than the inverse multiplicity ratio, the naive background baseline. This indicates the potential existence of a CME signal and the presence of remaining nonflow background due to two- and three-particle correlations, which are different between the isobars. In this postblind analysis, we estimate the contributions from those nonflow correlations as a background baseline to Y , utilizing the isobar data as well as Heavy Ion Jet Interaction Generator simulations. This baseline is found consistent with the isobar ratio measurement, and an upper limit of 10% at 95% confidence level is extracted for the CME fraction in the charge separation measurement in isobar collisions at s NN = 200 GeV. Published by the American Physical Society 2024
73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
Chiral symmetry and Atiyah-Patodi-Singer index theorem for staggered fermions
We consider the Atiyah-Patodi-Singer (APS) index theorem corresponding to the chiral symmetry of a continuum formulation of staggered fermions called Kähler-Dirac fermions, which have been recently investigated as an ingredient in lattice constructions of chiral gauge theories. We point out that there are two notions of chiral symmetry for Kähler-Dirac fermions, both having a mixed perturbative anomaly with gravity leading to index theorems on closed manifolds. By formulating these theories on a manifold with boundary, we find the APS index theorems corresponding to each of these symmetries, necessary for a complete picture of anomaly inflow, using a recently discovered physics-motivated proof. We comment on a fundamental difference between the nature of these two symmetries by showing that a sensible local, symmetric boundary condition only exists for one of the two symmetries. This sheds light on how these symmetries behave under lattice discretization, and in particular on their use for recent symmetric-mass generation proposals.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Exploring self-consistency of the equations of axion electrodynamics in Weyl semimetals
Recent works have provided evidence that an axial anomaly can arise in Weyl semimetals. If this is the case, then the electromagnetic response of Weyl semimetals should be governed by the equations of axion electrodynamics. These equations capture both the chiral magnetic and anomalous Hall effects in the limit of linear response, while at higher orders their solutions can provide detectable electromagnetic signatures of the anomaly. In this work, we consider three versions of axion electrodynamics that have been proposed in the Weyl semimetal literature. These versions differ in the form of the chiral magnetic term and in whether or not the axion is treated as a dynamical field. In each case, we look for solutions to these equations for simple sample geometries subject to applied external fields. We find that in the case of a linear chiral magnetic term generated by a nondynamical axion, self-consistent solutions can generally be obtained. In this case, the magnetic field inside of the Weyl semimetal can be magnified significantly, providing a testable signature for experiments. Self-consistent solutions can also be obtained for dynamical axions, but only in cases where the chiral magnetic term vanishes identically. Finally, for a nonlinear form of the chiral magnetic term frequently considered in the literature, we find that there are no self-consistent solutions aside from a few special cases.
75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
Anomalous hydrodynamics effective actions from holography
We derive an effective action for charged plasmas with an anomalous (abelian) global current charge current using holography. The holographic description is captured by the dynamics of an Einstein-Maxwell-Chern-Simons theory in an asymptotically AdS spacetime. The ’t Hooft anomaly contribution, which is encoded in the Chern-Simons term, contributes at the Gaussian order in the effective action only in the momentum diffusion sector, where it leads to chiral shear waves. However, as we demonstrate, beyond the Gaussian order, there is non-trivial imprint of the parity-violating anomaly term in sound and charge diffusion dynamics as well.
79 ASTRONOMY AND ASTROPHYSICS↗
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↗
Anomalies, a mod 2 index, and dynamics of 2d adjoint QCD
We show that 2 2 d adjoint QCD, an SU(N) S U ( N ) gauge theory with one massless adjoint Majorana fermion, has a variety of mixed ’t Hooft anomalies. The anomalies are derived using a recent mod 2 2 index theorem and its generalization that incorporates ’t Hooft flux. Anomaly matching and dynamical considerations are used to determine the ground-state structure of the theory. The anomalies, which are present for most values of N N , are matched by spontaneous chiral symmetry breaking. We find that massless 2 2 d adjoint QCD confines for N >2 N > 2 , except for test charges of N N -ality N/2 N / 2 , which are deconfined. In other words, \mathbb Z_N ℤ N center symmetry is unbroken for odd N N and spontaneously broken to \mathbb Z_{N/2} ℤ N / 2 for even N N . All of these results are confirmed by explicit calculations on small \mathbb{R}\times S^1 ℝ × S 1 . We also show that this non-supersymmetric theory exhibits exact Bose-Fermi degeneracies for all states, including the vacua, when N N is even. Furthermore, for most values of N N , 2 2 d massive adjoint QCD describes a non-trivial symmetry-protected topological (SPT) phase of matter, including certain cases where the number of interacting Majorana fermions is a multiple of 8 8 . As a result, it fits into the classification of (1+1) ( 1 + 1 ) d SPT phases of interacting Majorana fermions in an interesting way.
72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
Majorana chain and Ising model - (non-invertible) translations, anomalies, and emanant symmetries
We study the symmetries of closed Majorana chains in 1+1d, including the translation, fermion parity, spatial parity, and time-reversal symmetries. The algebra of the symmetry operators is realized projectively on the Hilbert space, signaling anomalies on the lattice, and constraining the long-distance behavior. In the special case of the free Hamiltonian (and small deformations thereof), the continuum limit is the 1+1d free Majorana CFT. Its continuum chiral fermion parity (-1)^{F_L} ( − 1 ) F L emanates from the lattice translation symmetry. We find a lattice precursor of its mod 8 ’t Hooft anomaly. Using a Jordan-Wigner transformation, we sum over the spin structures of the lattice model (a procedure known as the GSO projection), while carefully tracking the global symmetries. In the resulting bosonic model of Ising spins, the Majorana translation operator leads to a non-invertible lattice translation symmetry at the critical point. The non-invertible Kramers-Wannier duality operator of the continuum Ising CFT emanates from this non-invertible lattice translation of the transverse-field Ising model.
Physics↗
Noninvertible chiral symmetry and axions under electromagnetic duality
We study the implications of noninvertible chiral symmetry in a four-dimensional U(1) gauge theory coupled to massless fermions with electromagnetic 𝑆𝐿(2,ℤ) duality. This is done by deriving the Adler-Bell-Jackiw anomaly of massless QED in the dual frame that is used to explicitly construct the symmetry defect operator as well as the conserved two-form symmetry current. As expected, the noninvertible chiral symmetry is covariant under the duality transformation. This has implications for understanding the nature of kinetic and topological terms in the dual frame and for axion electrodynamics. In particular, we show that to generate an axion potential from a dyon loop, the one-form magnetic symmetry must be explicitly broken by a mutually nonlocal charged state with nonzero pairwise helicity.
Anomalies↗