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DOE OSTI2019

A Finite-Element Approach for the Partitioning of Carbon in Q&P Steel

This paper reports a Galerkin finite-element analysis of carbon partitioning from martensite into austenite during the quenching and partitioning (Q&P) processes in steels. In contrast to classical or sophisticated diffusion field models, an alternative nonlinear governing equation based on chemical potential and composition is considered. The model is applied to simulate the carbon partitioning of modified 22MnB5 alloys assuming an immobile austenite–martensite phase boundary and, in turn, is compared with experimental measurements of the volume fraction and carbon content of retained austenite. The simulations show outstanding results on the influence of Si and C content on the partitioning parameters.

36 MATERIALS SCIENCE↗

DOE OSTI2015

Characterization of transition carbides in quench and partitioned steel microstructures by Mössbauer spectroscopy and complementary techniques

Quenching and partitioning (Q&P) produces steel microstructures with martensite and austenite that exhibit promising property combinations for third generation advanced high strength steels. Understanding the kinetics of reactions that compete for available carbon, such as carbide formation, is critical for alloying and processing design and achieving austenite enrichment and retention during Q&P. Mössbauer effect spectroscopy (MES) was used to characterize Q&P microstructures in a 0.38C-1.54Mn-1.48Si wt.% steel after quenching to 225 °C and partitioning at 400 °C for 10 or 300 s, with an emphasis on transition carbides. The recoilless fraction for η-carbide was calculated and a correction for saturation of the MES absorption spectrum was applied, making quantitative measurements of small amounts of η-carbide, including non-stoichiometric η-carbide, possible in Q&P microstructures. Complementary transmission electron microscopy confirmed the presence of η-carbides, and MES and X-ray diffraction were used to characterize the austenite. The amount of η-carbide formed during Q&P ranged from 1.4 to 2.4 at.%, accounting for a substantial portion (~24% to 41%) of the bulk carbon content of the steel. The amount (5.0 at.%) of η-carbide that formed after quenching and tempering (Q&T) at 400 °C for 300 s was significantly greater than after partitioning at 400 °C for 300 s (2.4 at.%), suggesting that carbon partitioning from martensite to austenite occurs in conjunction with η-carbide formation during Q&P in these specimens.

36 MATERIALS SCIENCE↗

DOE OSTI2015

Austenite stabilization and high strength-elongation product of a low silicon aluminum-free hot-rolled directly quenched and dynamically partitioned steel

Microstructures composed of lath martensite and retained austenite with volume fraction between 8.0 vol.% and 12.0 vol.% were obtained in a low-C low-Si Al-free steel through hot-rolling direct quenching and dynamical partitioning (HDQ&DP) processes. The austenite stabilization mechanism in the low-C low-Si Al-free steel under the special dynamical partitioning processes is investigated by analyzing the carbon partition behavior from martensite to austenite and the carbide precipitation-coarsening behavior in martensite laths combining with the possible hot rolling deformation inheritance. Results show that the satisfying retained austenite amount in currently studied low-Si Al-free HDQ&DP steel is caused by the high-efficiency carbon enrichment in the 30–80 nm thick regions of austenite near the interfaces in the hot-rolled ultra-fast cooled structure and the avoidance of serious carbides coarsening during the continuous cooling procedures. The excellent strength-elongation product reaching up to 26,000 MPa% shows that the involved HDQ&DP process is a promising method to develop a new generation of advanced high strength steel. - Highlights: • HDQ&DP processes were applied to a low-C low-Si Al-free steel. • Effective partitioning time during the continuous cooling processes is 1–220 s. • Retained austenite with volume fraction between 8.0 vol. % and 12.0 vol. % has been obtained. • The special austenite stabilization mechanism has been expounded.

36 MATERIALS SCIENCE↗

DOE OSTI2020

Exploring the Role of Inorganic and Organic Interfaces on CO 2 and CH 4 Partitioning: Case Study of Silica, Illite, Calcite, and Kerogen Nanopores on Gas Adsorption and Nanoscale Transport Behaviors

The adsorption, partitioning, and diffusion of CO 2 and CH 4 in organic–inorganic pores composed of kerogen with silica, illite, or calcite are studied using density functional theory and classical molecular dynamics simulations. The adsorption and partitioning behavior of CO 2 and CH 4 molecules is found to be a function of chemistry of the solid interface, pore size, and surface area. CO 2 molecules are preferentially adsorbed compared to CH 4 molecules on silica, illite, calcite, and kerogen surfaces due to significant contributions of electrostatic interactions with the atoms of the associated surfaces. CO 2 and CH 4 molecules display higher adsorption energy on calcite and silica compared to those on illite and kerogen because of enhanced interactions with the positively charged calcium ions on the calcite surface and the hydroxyl group (-OH) on the silica surface. Enhanced internal nanopores and the availability of adsorption active sites in illite and kerogen matrices aid in higher partitioning of the gas molecules into these pores. CO 2 has a significant influence on the clustering and swelling of kerogen fragments compared to CH 4 . Higher CO 2 adsorption on inorganic and kerogen surfaces results in lower overall self-diffusivities compared to CH 4 . This study illustrates surface and pore size controls on the adsorption, partitioning, and self-diffusivities of CO 2 and CH 4 at conditions relevant for subsurface energy applications. The chemistry of the surfaces along with the availability of internal pores and active adsorption sites influences the adsorption behavior of gases. Our results suggest that CO 2 stored in depleted gas reservoirs may preferentially inhabit nanoconfined pores.

37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CH↗

DOE OSTI2016

Determination of Organic Partitioning Coefficients in Water-Supercritical CO 2 Systems by Simultaneous in Situ UV and Near-Infrared Spectroscopies

CO2 injected into depleted oil or gas reservoirs for long-term storage has the potential to mobilize organic compounds and distribute them between sediments and reservoir brines. Understanding this process is important when considering health and environmental risks, but little quantitative data currently exists on the partitioning of organics between supercritical CO2 and water. In this work, a high-pressure, in situ measurement capability was developed to assess the distribution of organics between CO2 and water at conditions relevant to deep underground storage of CO2. The apparatus consists of a titanium reactor with quartz windows, near-infrared and UV spectroscopic detectors, and switching valves that facilitate quantitative injection of organic reagents into the pressurized reactor. To demonstrate the utility of the system, partitioning coefficients were determined for benzene in water/supercritical CO2 over the range 35-65 °C and approximately 25-150 bar. Density changes in the CO2 phase with increasing pressure were shown to have dramatic impacts on benzene's partitioning behavior. Our partitioning coefficients were approximately 5-15 times lower than values previously determined by ex situ techniques that are prone to sampling losses. The in situ methodology reported here could be applied to quantify the distribution behavior of a wide range of organic compounds that may be present in geologic CO2 storage scenarios.

Environmental Molecular Sciences Laboratory↗

DOE OSTI2015

The total position-spread tensor: Spin partition

The Total Position Spread (TPS) tensor, defined as the second moment cumulant of the position operator, is a key quantity to describe the mobility of electrons in a molecule or an extended system. In the present investigation, the partition of the TPS tensor according to spin variables is derived and discussed. It is shown that, while the spin-summed TPS gives information on charge mobility, the spin-partitioned TPS tensor becomes a powerful tool that provides information about spin fluctuations. The case of the hydrogen molecule is treated, both analytically, by using a 1s Slater-type orbital, and numerically, at Full Configuration Interaction (FCI) level with a V6Z basis set. It is found that, for very large inter-nuclear distances, the partitioned tensor growths quadratically with the distance in some of the low-lying electronic states. This fact is related to the presence of entanglement in the wave function. Non-dimerized open chains described by a model Hubbard Hamiltonian and linear hydrogen chains H{sub n} (n ≥ 2), composed of equally spaced atoms, are also studied at FCI level. The hydrogen systems show the presence of marked maxima for the spin-summed TPS (corresponding to a high charge mobility) when the inter-nuclear distance is about 2 bohrs. This fact can be associated to the presence of a Mott transition occurring in this region. The spin-partitioned TPS tensor, on the other hand, has a quadratical growth at long distances, a fact that corresponds to the high spin mobility in a magnetic system.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗

DOE OSTI2020

Partitioning net carbon dioxide fluxes into photosynthesis and respiration using neural networks

The eddy covariance (EC) technique is used to measure the net ecosystem exchange (NEE) of CO 2 between ecosystems and the atmosphere, offering a unique opportunity to study ecosystem responses to climate change. NEE is the difference between the total CO 2 release due to all respiration processes (RECO), and the gross carbon uptake by photosynthesis (GPP). These two gross CO 2 fluxes are derived from EC measurements by applying partitioning methods that rely on physiologically based functional relationships with a limited number of environmental drivers. However, the partitioning methods applied in the global FLUXNET network of EC observations do not account for the multiple co-acting factors that modulate GPP and RECO flux dynamics. To overcome this limitation, we developed a hybrid data-driven approach based on combined neural networks (NN C-part ). NN C-part incorporates process knowledge by introducing a photosynthetic response based on the light-use efficiency (LUE) concept, and uses a comprehensive dataset of soil and micrometeorological variables as fluxes drivers. We applied the method to 36 sites from the FLUXNET2015 dataset and found a high consistency in the results with those derived from other standard partitioning methods for both GPP (R 2 > .94) and RECO (R 2 > .8). High consistency was also found for (a) the diurnal and seasonal patterns of fluxes and (b) the ecosystem functional responses. NNC-part performed more realistic than the traditional methods for predicting additional patterns of gross CO 2 fluxes, such as: (a) the GPP response to VPD, (b) direct effects of air temperature on GPP dynamics, (c) hysteresis in the diel cycle of gross CO 2 fluxes, (d) the sensitivity of LUE to the diffuse to direct radiation ratio, and (e) the post rain respiration pulse after a long dry period. In conclusion, NN C-part is a valid data-driven approach to provide GPP and RECO estimates and complementary to the existing partitioning methods.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2018

Improving Unstructured Mesh Partitions for Multiple Criteria Using Mesh Adjacencies

The scalability of unstructured mesh based applications depends on partitioning methods that quickly balance the computational work while reducing communication costs. Zhou et al. [SIAM J. Sci. Comput., 32 (2010), pp. 3201{3227; J. Supercomput., 59 (2012), pp. 1218{1228] demonstrated the combination of (hyper)graph methods with vertex and element partition improvement for PHASTA CFD scaling to hundreds of thousands of processes. Our work generalizes partition improvement to support balancing combinations of all the mesh entity dimensions (vertices, edges, faces, regions) in partitions with imbalances exceeding 70%. Improvement results are then presented for multiple entity dimensions on up to one million processes on meshes with over 12 billion tetrahedral elements.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2024

Partitioning of Fe(II) in reduced nontronite (NAu-2) to reactive sites: Reactivity in terms of Tc(VII) reduction

Abstract Clay minerals impart important chemical properties to soils, in part, by virtue of changes in the redox state of Fe in their crystal structures. Therefore, measurement of Fe(III)/Fe(II) and partitioning of Fe(II) in different reactive sites in clay minerals (during biological and chemical Fe(III) reduction) is essential to understand their role and their relative reactivity in terms of reduction and immobilization of heavy metal contaminants such as technetium. This study had three objectives: (1) to understand the degree of dissolution of nontronite (Fe-rich smectite) as a result of chemical and biological reduction of Fe(III) in the structure; (2) to quantify partitioning of chemically and biologically produced Fe(II) into different reactive sites in reduced nontronite, including aqueous Fe 2+ , ammonium chloride-extractable Fe(II) (mainly from the ion-exchangeable sites, denoted as Fe ( II ) NH 4 Cl ${\rm{Fe}}{\left( {{\rm{II}}} \right)_{{\rm{N}}{{\rm{H}}_4}{\rm{Cl}}}}$ ), sodium acetate-extractable Fe(II) (mainly from the surface complexation sites, denoted as Fe(II) acetate ), and structural Fe(II) (denoted as Fe(II) str ); and (3) to evaluate the reactivity of these Fe(II) species in terms of Tc(VII) reduction. Chemical and biological reduction of Fe(III) in nontronite (NAu-2) was performed, and reduced nontronite samples with different extents of Fe(III) reduction (1.2–71%) were prepared. The extent of reductive dissolution was measured as a function of the extent of Fe(III) reduction. Our results demonstrated that chemically and biologically produced Fe(II) in NAu-2 may be accommodated in the NAu-2 structure if the extent of Fe(III) reduction is small (< ∼30%). When the extent of reduction was >∼30%, dissolution of nontronite occurred with a corresponding decrease in crystallinity of residual nontronite. The Fe(II) produced was available for partitioning into four species: Fe ( ab ) 2 + ${\rm{Fe}}_{\left( {{\rm{ab}}} \right)}^{2 + }$ , Fe(II) acetate , Fe ( II ) NH 4 Cl ${\rm{Fe}}{\left( {{\rm{II}}} \right)_{{\rm{N}}{{\rm{H}}_4}{\rm{Cl}}}}$ , and Fe(II) str . The increase in Fe(II) acetate during the early stages of Fe(III) reduction indicated that the Fe(II) released had the greatest affinity for the surface-complexation sites, but this site had a limited capacity (∼60 µmol of Fe(II)/g of NAu-2). The subsequent increase in Fe ( II ) NH 4 Cl ${\rm{Fe}}{\left( {{\rm{II}}} \right)_{{\rm{N}}{{\rm{H}}_4}{\rm{Cl}}}}$ indicated that the released Fe(II) partitioned into the exchangeable sites once the amount of Fe at the surface-complexation sites reached half of its maximum site capacity. The fraction of Fe(II) str decreased concomitantly, as a result of Fe(II) release from the NAu-2 structure, from 100% when the extent of Fe(III) reduction was <30% to nearly 65% when the extent of Fe(III) reduction reached 71%. The Fe(II) acetate and Fe(II) str exhibited greater reactivity in terms of Tc(VII) reduction than the Fe ( II ) NH 4 Cl ${\rm{Fe}}{\left( {{\rm{II}}} \right)_{{\rm{N}}{{\rm{H}}_4}{\rm{Cl}}}}$ . Clearly, the surface-complexed and structural Fe(II) are the desirable species when reduced clay minerals are used to reduce and immobilize soluble heavy metals in contaminated groundwater and soils. These results have important implications for understanding microbe—clay mineral interactions and heavy metal immobilization in clay-rich natural environments.

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2016

Partitioning CO 2 fluxes with isotopologue measurements and modeling to understand mechanisms of forest carbon sequestration

1. Objectives This project combines automated in situ observations of the isotopologues of CO 2 with root observations, novel experimental manipulations of belowground processes, and isotope-enabled ecosystem modeling to investigate mechanisms of below- vs. aboveground carbon sequestration at the Harvard Forest Environmental Measurements Site (EMS). The proposed objectives, which have now been largely accomplished, include: A. Partitioning of net ecosystem CO 2 exchange (NEE) into photosynthesis and respiration using long-term continuous observations of the isotopic composition of NEE, and analysis of their dynamics ; B. Investigation of the influence of vegetation phenology on the timing and magnitude of carbon allocated belowground using measurements of root growth and indices of belowground autotrophic vs. heterotrophic respiration (via trenched plots and isotope measurements); C. Testing whether plant allocation of carbon belowground stimulates the microbial decomposition of soil organic matter, using in situ rhizosphere simulation experiments wherein realistic quantities of artificial isotopically-labeled exudates are released into the soil; and D. Synthesis and interpretation of the above data using the Ecosystem Demography Model 2 (ED2). 2. Highlights Accomplishments: • Our isotopic eddy flux record has completed its 5th full year and has been used to independently estimate ecosystem-scale respiration and photosynthesis. • Soil surface chamber isotopic flux measurements were carried out during three growing seasons, in conjunction with a trenching manipulation. Key findings to date (listed by objective): A. Partitioning of Net Ecosystem Exchange: 1. Ecosystem respiration is lower during the day than at night—the first robust evidence of the inhibition of leaf respiration by light (the “Kok effect”) at the ecosystem scale. 2. Because it neglects the Kok effect, the standard NEE partitioning approach overestimates ecosystem photosynthesis (by ~25%) and daytime respiration (by ~100%) in the first half of the growing season at our site, and portrays ecosystem photosynthetic light-use efficiency as declining when in fact it is stable until autumnal senescence. B. Vegetation Phenology and belowground allocation: Findings: 1. Autotrophic respiration (Ra) showed a seasonal pattern, peaking in mid-summer when trees were most active. 2. The effective age of the substrate for belowground respiration is less than 2 weeks. 3. Above and belowground phenology are more synchronous in deciduous hardwood stands than evergreen hemlock stands. 4. The decline in root respiration rates in the fall is related to temperature rather than acclimation of root respiration or substrate limitations. Methodological Issues: 5. The isotopic signatures of autotrophic and heterotrophic respiration are too similar for isotopic partitioning of belowground respiration into these two components at our site—in keeping with the recent findings of Bowling et al. (2015) in a subalpine conifer forest. 6. Artifacts of the trenching method, such as changes in soil moisture and increased carbon substrate from the newly severed roots, are significant and need to be quantified when determining daily to annual estimates of autotrophic and heterotrophic respiration. C. Effects of simulated exudates on priming of microbial decomposition: The stoichiometry of root exudates influences both the amount and the mechanism by which priming occurs. At low C:N, SOC loss is caused by an increase in microbial efficiency. At high C:N, SOC loss is caused by an increase in microbial biomass. D. Modeling with the Ecosystem Demography Model (ED2): 1. Incorporation of 13C tracking to create an isotopically-enabled Ecosystem Demography v2 model (ED2) 2. State-of-the-art parameter optimization methodology developed for improving ED2 model predictions and parameters. 3. Significantly improved model predictions of growth- and maintenance-related carbon fluxes and 13C fluxes

54 ENVIRONMENTAL SCIENCES↗

DOE OSTI2022

Cloud Type and Life Stage Dependency of Liquid–Ice Mass Partitioning in Mixed-Phase Clouds

This paper analyzes the temperature, cloud type, and life stage dependencies of phase partitioning in mixed-phase clouds spanning tropics, midlatitudes, and the Arctic, using data from ground-based remote sensing measurements in Alaska and aircraft measurements from three field campaigns. The results show: (1) The liquid fraction in Arctic stratiform clouds decreased from 1 to 0.6 between 0 °C and −30 °C and was lower in spring because of the higher dust occurrence in Barrow, Alaska; (2) In wintertime orographic clouds, the liquid fraction was greater than 0.8; (3) Phase partitioning in convective clouds varied significantly with life stages. In the developing stage, it decreased from 1 to 0.3 between −5 °C and −15 °C, indicating rapid ice generation, while at the mature and dissipating stages, the liquid fractions were lower; (4) The stratiform regions of mesoscale convective systems were dominated by ice, with liquid fractions lower than 0.2; and (5) The variability of phase partitioning varied for different cloud types. In stratiform clouds, liquid dominated at warm temperatures. As the temperature decreased, an ice-dominated region was more frequently observed, while the occurrence of the mixed-phase region remained low. For convective clouds, the variability of phase partitioning was controlled by continuous glaciation with decreasing temperature and life cycle.

54 ENVIRONMENTAL SCIENCES↗

NASA NTRS2018

Attribution of Flux Partitioning Variations Between Land Surface Models over the Continental U.S.

Accurate quantification of the terrestrial evapotranspiration (ET) components of plant transpiration (T), soil evaporation (E) and evaporation of the intercepted water (I) is necessary for improving our understanding of the links between the carbon and water cycles. Recent studies have noted that, among the modeled estimates, large disagreements exist in the relative contributions of T, E and I to the total ET. As these models are often used in data assimilation environments for incorporating and extending ET relevant remote sensing measurements, understanding the sources of inter-model differences in ET components is also necessary for improving the utilization of such remote sensing measurements. This study quantifies the contributions of two key factors explaining inter-model disagreements to the uncertainty in total ET: (1) contribution of the local partitioning and (2) regional distribution of ET. The analysis is conducted by using outputs from a suite of land surface models in the North American Land Data Assimilation System (NLDAS) configuration. For most of these models, transpiration is the dominant component of the ET partition. The results indicate that the uncertainty in local partitioning dominates the inter-model spread in modeled soil evaporation E. The inter-model differences in T are dominated by the uncertainty in the distribution of ET over the Eastern U.S. and the local partitioning uncertainty in the Western U.S. The results also indicate that uncertainty in the T estimates is the primary driver of total ET errors. Over the majority of the U.S., the contribution of the two factors of uncertainty to the overall uncertainty is non-trivial.

uncertainty↗

NASA NTRS2018

Attribution of Flux Partitioning Variations Between Land Surface Models Over the Continental U.S.

evapotranspiration partitioning; transpiration; so↗

DOE OSTI2015

Multi-jagged: A scalable parallel spatial partitioning algorithm

Geometric partitioning is fast and effective for load-balancing dynamic applications, particularly those requiring geometric locality of data (particle methods, crash simulations). We present, to our knowledge, the first parallel implementation of a multidimensional-jagged geometric partitioner. In contrast to the traditional recursive coordinate bisection algorithm (RCB), which recursively bisects subdomains perpendicular to their longest dimension until the desired number of parts is obtained, our algorithm does recursive multi-section with a given number of parts in each dimension. By computing multiple cut lines concurrently and intelligently deciding when to migrate data while computing the partition, we minimize data movement compared to efficient implementations of recursive bisection. We demonstrate the algorithm's scalability and quality relative to the RCB implementation in Zoltan on both real and synthetic datasets. Our experiments show that the proposed algorithm performs and scales better than RCB in terms of run-time without degrading the load balance. Lastly, our implementation partitions 24 billion points into 65,536 parts within a few seconds and exhibits near perfect weak scaling up to 6K cores.

97 MATHEMATICS AND COMPUTING↗

DOE OSTI2016

Experimental evidence for melt partitioning between olivine and orthopyroxene in partially molten harzburgite

Abstract Observations of dunite channels in ophiolites and uranium series disequilibria in mid‐ocean ridge basalt suggest that melt transport in the upper mantle beneath mid‐ocean ridges is strongly channelized. We present experimental evidence that spatial variations in mineralogy can also focus melt on the grain scale. This lithologic melt partitioning, which results from differences in the interfacial energies associated with olivine‐melt and orthopyroxene‐melt boundaries, may complement other melt focusing mechanisms in the upper mantle such as mechanical shear and pyroxene dissolution. We document here lithologic melt partitioning in olivine‐/orthopyroxene‐basaltic melt samples containing nominal olivine to orthopyroxene ratio of 3 to 2 and melt fractions of 0.02 to 0.20. Experimental samples were imaged using synchrotron‐based X‐ray microcomputed tomography at a resolution of 700 nm per voxel. By analyzing the local melt fraction distributions associated with olivine and orthopyroxene grains in each sample, we found that the melt partitioning coefficient, i.e., the ratio of melt fraction around olivine to that around orthopyroxene grains, varies between 1.1 and 1.6. The permeability and electrical conductivity of our digital samples were estimated using numerical models and compared to those of samples containing only olivine and basaltic melt. Our results suggest that lithologic melt partitioning and preferential localization of melt around olivine grains might play a role in melt focusing, potentially enhancing average melt ascent velocities.

Miller, Kevin J.↗

DOE OSTI2020

A Strategy for Constructing Pore‐Space‐Partitioned MOFs with High Uptake Capacity for C 2 Hydrocarbons and CO 2

Abstract Introduction of pore partition agents into hexagonal channels of MIL‐88 type (acs topology) endows materials with high tunability in gas sorption. Here, we report a strategy to partition acs framework into pacs (partitioned acs) crystalline porous materials (CPM). This strategy is based on insertion of in situ synthesized 4,4′‐dipyridylsulfide (dps) ligands. One third of open metal sites in the acs net are retained in pacs MOFs; two thirds are used for pore‐space partition. The Co 2 V‐pacs MOFs exhibit near or at record high uptake capacities for C 2 H 2 , C 2 H 4 , C 2 H 6 , and CO 2 among MOFs. The storage capacity of C 2 H 2 is 234 cm 3 g −1 (298 K) and 330 cm 3 g −1 (273 K) at 1 atm for CPM‐733‐dps (the Co 2 V‐BDC form, BDC=1,4‐benzenedicarboxylate). These high uptake capacities are accomplished with low heat of adsorption, a feature desirable for low‐energy‐cost adsorbent regeneration. CPM‐733‐dps is stable and shows no loss of C 2 H 2 adsorption capacity following multiple adsorption–desorption cycles.

Wang, Yong↗

DOE OSTI2018

Constraints on flavored 2d CFT partition functions

We study the implications of modular invariance on 2d CFT partition functions with abelian or non-abelian currents when chemical potentials for the charges are turned on, i.e. when the partition functions are “flavored”. We begin with a new proof of the transformation law for the modular transformation of such partition functions. Then we proceed to apply modular bootstrap techniques to constrain the spectrum of charged states in the theory. We improve previous upper bounds on the state with the greatest “mass-to-charge” ratio in such theories, as well as upper bounds on the weight of the lightest charged state and the charge of the weakest charged state in the theory. We apply the extremal functional method to theories that saturate such bounds, and in several cases we find the resulting prediction for the occupation numbers are precisely integers. Because such theories sometimes do not saturate a bound on the full space of states but do saturate a bound in the neutral sector of states, we find that adding flavor allows the extremal functional method to solve for some partition functions that would not be accessible to it otherwise.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗

DOE OSTI2016

High-temperature asymptotics of supersymmetric partition functions

We study the supersymmetric partition function of 4d supersymmetric gauge theories with a U(1) R-symmetry on Euclidean S 3 × S β 1 , with S 3 the unit-radius squashed three-sphere, and β the circumference of the circle. For superconformal theories, this partition function coincides (up to a Casimir energy factor) with the 4d superconformal index. The partition function can be computed exactly using the supersymmetric localization of the gauge theory path-integral. It takes the form of an elliptic hypergeometric integral, which may be viewed as a matrix-integral over the moduli space of the holonomies of the gauge fields around S β 1 . At high temperatures (β → 0, corresponding to the hyperbolic limit of the elliptic hypergeometric integral) we obtain from the matrix-integral a quantum effective potential for the holonomies. The effective potential is proportional to the temperature. Therefore the high-temperature limit further localizes the matrix-integral to the locus of the minima of the potential. If the effective potential is positive semi-definite, the leading high-temperature asymptotics of the partition function is given by the formula of Di Pietro and Komargodski, and the subleading asymptotics is connected to the Coulomb branch dynamics on R 3 × S 1 . In theories where the effective potential is not positive semi-definite, the Di Pietro-Komargodski formula needs to be modified. In particular, this modification occurs in the SU(2) theory of Intriligator-Seiberg-Shenker, and the SO(N) theory of Brodie-Cho-Intriligator, both believed to exhibit “misleading” anomaly matchings, and both believed to yield interacting superconformal field theories with c < a. Lastly, two new simple tests for dualities between 4d supersymmetric gauge theories emerge as byproducts of our analysis.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗