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Search indexed NASA NTRS and DOE OSTI research on propulsion, heat transfer, battery materials and energy systems. Follow report and document links to the original sources.

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At least 55 records · Page 3
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DOE OSTI2022

Characters, quasinormal modes, and Schwinger pairs in dS 2 with flux

An integral representation of the 1-loop partition function for charged scalars and spinors, minimally coupled to a uniform U(1) field on S 2 , is given in terms of SO(1, 2) Harish-Chandra group characters and evaluated exactly in terms of Hurwitz ζ-functions. Analytically continuing the U(1) field, we interpret the path integrals as quasicanonical partition functions in dS 2 with an electric field. The character itself is obtained as a trace over states living at the future boundary of de Sitter and has a quasinormal mode expansion. The imaginary part of the partition function captures Schwinger pair creation in the static patch at finite temperature. The thermal enhancement is most noticeable for scalar masses below Hubble and leads to non-monotonicity of the current as a function of the field. This parameter range, when dimensionally reducing from a charged or rotating Nariai spacetime, is excluded by Swampland-inspired bounds. Around the AdS 2 black hole, in contrast to dS 2 , there is a threshold to pair creation.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2024

Angular fractals in thermal QFT

We show that thermal effective field theory controls the long-distance expansion of the partition function of a d-dimensional QFT, with an insertion of any finite-order spatial isometry. Consequently, the thermal partition function on a sphere displays a fractal-like structure as a function of angular twist, reminiscent of the behavior of a modular form near the real line. As an example application, we find that for CFTs, the effective free energy of even-spin minus odd-spin operators at high temperature is smaller than the usual free energy by a factor of 1/2 d . Near certain rational angles, the partition function receives subleading contributions from “Kaluza-Klein vortex defects” in the thermal EFT, which we classify. We illustrate our results with examples in free and holographic theories, and also discuss nonperturbative corrections from worldline instantons.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Replica symmetry breaking for the integrable two-site Sachdev–Ye–Kitaev model

We analyze a two-body non-Hermitian two-site Sachdev–Ye–Kitaev (SYK) model with the couplings of one site complex conjugated to the other site. This model, with no explicit coupling between the sites, shows an infinite number of second-order phase transitions, which is a consequence of the factorization of the partition function into a product over Matsubara frequencies. We calculate the quenched free energy in two different ways: first in terms of the single-particle energies and second by solving the Schwinger–Dyson equations of the two-site model. The first calculation can be done entirely in terms of a one-site model. The conjugate replica enters due to non-analyticities when Matsubara frequencies enter the spectral support of the coupling matrix. The second calculation is based on the replica trick of the two-site partition function. Both methods give the same result. The free-fermion partition function can also be rephrased as a matrix model for the coupling matrix. Up to minor details, this model is the random matrix model that describes the chiral phase transition of QCD, and the order parameter of the two-body model corresponds to the chiral condensate of QCD. Comparing to the corresponding four-body model, we are able to determine which features of the free energy are due to the chaotic nature of the four-body model. The high-temperature phase of both models is entropy dominated, and in both cases, the free energy is determined by the spectral density. The chaotic four-body SYK model has a low-temperature phase whose free energy is almost temperature-independent, signaling an effective gap of the theory even though the actual spectrum does not exhibit a gap. On the other hand, the low-temperature free energy of the two-body SYK model is not flat; in fact, it oscillates to arbitrarily low temperature. This indicates a less desirable feature that the entropy of the two-body model is not always positive in the low-temperature phase, which most likely is a consequence of the non-hermiticity.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2020

Normal modes in thermal AdS via the Selberg zeta function

The heat kernel and quasinormal mode methods of computing 1-loop partition functions of spin s s fields on hyperbolic quotient spacetimes \mathbb{H}^{3}/\mathbb{Z} ℍ 3 / ℤ are related via the Selberg zeta function. We extend that analysis to thermal \text{AdS}_{2n+1} AdS 2 n + 1 backgrounds, with quotient structure \mathbb{H}^{2n+1}/\mathbb{Z} ℍ 2 n + 1 / ℤ . Specifically, we demonstrate the zeros of the Selberg function encode the normal mode frequencies of spin fields upon removal of non-square-integrable modes. With this information we construct the 1-loop partition functions for symmetric transverse traceless tensors in terms of the Selberg zeta function and find exact agreement with the heat kernel method.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Lectures on statistical mechanics

Presented here is a transcription of the lecture notes from Professor Allan N. Kaufman’s graduate statistical mechanics course Physics 212A and 212B at the University of California Berkeley from the 1972–1973 academic year. 212A addressed equilibrium statistical mechanics with topics: fundamentals (micro-canonical and sub-canonical ensembles, adiabatic law and action conservation, fluctuations, pressure, and virial theorem), classical fluids and other systems (equation of state, deviations from ideality, virial coefficients and van der Waals potential, canonical ensemble and partition function, quasistatic evolution, grand-canonical ensemble and partition function, chemical potential, simple model of a phase transition, quantum virial expansion, numerical simulation of equations of state, and phase transition), chemical equilibrium (systems with multiple species and chemical reactions, law of mass action, Saha equation, chemical equilibrium including ionization and excited states), and long-range interactions (including Coulomb, dipole, and gravitational interactions, Debye–Hückel theory, and shielding). 212B addressed nonequilibrium statistical mechanics with topics: fundamentals (definitions: realizations, moments, characteristic function, and discrete variables), Brownian motion (Langevin equation, fluctuation–dissipation theorem, spatial diffusion, Boltzmann’s H-theorem), Liouville and Klimontovich equations, Landau equation (derivation, elaboration, and H-theorem, and irreversibility), Markov processes and Fokker–Planck equation (derivations of the Fokker–Planck equation and a master equation), linear response and transport theory (linear Boltzmann equation, linear response theory of Kubo and Mori, relation of entropy production to electrical conductivity, transport relations and coefficients, normal mode solutions of the transport equations, sketch of a generalized Langevin equation method for transport theory), and an introduction to nonequilibrium quantum statistical mechanics.

plasma dynamics↗
DOE OSTI2025

QCD Constraints on Isospin-Dense Matter and the Nuclear Equation of State

Understanding the behavior of dense hadronic matter is a central goal in nuclear physics as it governs the nature and dynamics of astrophysical objects such as supernovae and neutron stars. Because of the nonperturbative nature of quantum chromodynamics (QCD), little is known rigorously about hadronic matter in these extreme conditions. Here, lattice QCD calculations are used to compute thermodynamic quantities and the equation of state of QCD over a wide range of isospin chemical potentials with controlled systematic uncertainties. Agreement is seen with chiral perturbation theory when the chemical potential is small. Comparison to perturbative QCD at large chemical potential allows for an estimate of the gap in the superconducting phase, and this quantity is seen to agree with perturbative determinations. Since the partition function for an isospin chemical potential μ I bounds the partition function for a baryon chemical potential μ B = 3 μ I / 2 , these calculations also provide rigorous nonperturbative QCD bounds on the symmetric nuclear matter equation of state over a wide range of baryon densities for the first time. Published by the American Physical Society 2025

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗
DOE OSTI2021

Chern-Simons invariants from ensemble averages

We discuss ensemble averages of two-dimensional conformal field theories associated with an arbitrary indefinite lattice with integral quadratic form Q. We provide evidence that the holographic dual after the ensemble average is the three-dimensional Abelian Chern-Simons theory with kinetic term determined by Q. The resulting partition function can be written as a modular form, expressed as a sum over the partition functions of Chern-Simons theories on lens spaces. For odd lattices, the dual bulk theory is a spin Chern-Simons theory, and we identify several novel phenomena in this case. We also discuss the holographic duality prior to averaging in terms of Maxwell-Chern-Simons theories.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Chiral algebra, localization, modularity, surface defects, and all that

We study the 2D vertex operator algebra (VOA) construction in 4D N = 2 superconformal field theories on S 3 × S 1 , focusing on both old puzzles and new observations. The VOA lives on a two-torus T 2 ⊂ S 3 × S 1 , it is 1 2 Z -graded, and this torus is equipped with the natural choice of spin structure (1,0) for the Z + 1 2 -graded operators, corresponding to the NS sector vacuum character. By analyzing the possible refinements of the Schur index that preserves the VOA, we find that it admits discrete deformations, which allows access to the remaining spin structures (1,1), (0,1), and (0,0), of which the latter two involve the inclusion of a particular surface defect. For Lagrangian theories, we perform the detailed analysis: we describe the natural supersymmetric background, perform localization, and derive the gauged symplectic boson action on a torus in any spin structure. In the absence of flavor fugacities, the 2D and 4D path integrals precisely match, including the Casimir factors. We further analyze the 2D theory: we identify its integration cycle and the two-point functions and interpret flavor holonomies as screening charges in the VOA. Next, we make some observations about modularity; the T-transformation acts on our four partition functions and lifts to a large diffeomorphism on S 3 × S 1 . More interestingly, we generalize the four partition functions on the torus to an infinite family labeled by both the spin structure and the integration cycle inside the complexified maximal torus of the gauge group. Members of this family transform into one another under the full modular group, and we confirm the recent observation that the S-transform of the Schur index in Lagrangian theories exhibits logarithmic behavior. Finally, we comment on how locally our background reproduces the Ω-background.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2024

Spin-statistics for black hole microstates

The gravitational path integral can be used to compute the number of black hole states for a given energy window, or the free energy in a thermal ensemble. In this article we explain how to use the gravitational path integral to compute the separate number of bosonic and fermionic black hole microstates. We do this by comparing the partition function with and without the insertion of (–1) F . In particular we introduce a universal rotating black hole that contributes to the partition function in the presence of (–1) F. We study this problem for black holes in asymptotically flat space and in AdS, putting constraints on the high energy spectrum of holographic CFTs (not necessarily supersymmetric). Finally, we analyze wormhole contributions to related quantities.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

The statistical mechanics of near-BPS black holes

Due to the failure of thermodynamics for low temperature near-extremal black holes, it has long been conjectured that a 'thermodynamic mass gap' exists between an extremal black hole and the lightest near-extremal state. For non-supersymmetric near-extremal black holes in Einstein gravity with an AdS2 throat, no such gap was found. Rather, at that energy scale, the spectrum exhibits a continuum of states, up to non-perturbative corrections. In this paper, we compute the partition function of near-BPS black holes in supergravity where the emergent, broken, symmetry is PSU(1, 1|2). To reliably compute this partition function, we show that the gravitational path integral can be reduced to that of a $\mathcal{N}=4$ supersymmetric extension of the Schwarzian theory, which we define and exactly quantize. In contrast to the non-supersymmetric case, we find that black holes in supergravity have a mass gap and a large extremal black hole degeneracy consistent with the Bekenstein–Hawking area. Furthermore, our results verify a plethora of string theory conjectures, concerning the scale of the mass gap and the counting of extremal micro-states.

79 ASTRONOMY AND ASTROPHYSICS↗
DOE OSTI2021

Subleading corrections to the S 3 free energy of necklace quiver theories dual to massive IIA

We investigate the S 3 free energy of N = 3 Chern-Simons-matter quiver gauge theories with gauge group U(N) r (r ≥ 2) where the sum of Chern-Simons levels does not vanish, beyond the leading order in the large-N limit. We take two different approaches to explore the sub-leading structures of the free energy. First we evaluate the matrix integral for the partition function in the ’t Hooft limit using a saddle point approximation. Second we use an ideal Fermi-gas model to compute the same partition function, but in the limit of fixed Chern-Simons levels. The resulting expressions for the free energy F = – log Z are then compared in the overlapping parameter regime. The Fermi-gas approach also hints at a universal 1/6 log N correction to the free energy. Since the quiver gauge theories we consider are dual to massive Type IIA theory, we expect the sub-leading correction of the planar free energy in the large ’t Hooft parameter limit to match higher-derivative corrections to the tree-level holographic dual free energy, which have not yet been fully investigated.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Lessons from the Ramond sector

We revisit the consistency of torus partition functions in (1+1)d fermionic conformal field theories, combining old ingredients of modular invariance/covariance with a modernized understanding of bosonization/fermionization dualities. Various lessons can be learned by simply examining the oft-ignored Ramond sector. For several extremal/kinky modular functions in the bootstrap literature, we can either rule out or identify the underlying theory. We also revisit the N = 1 Maloney-Witten partition function by calculating the spectrum in the Ramond sector, and further extending it to include the modular sum of seed Ramond characters. Finally, we perform the full N = 1 RNS modular bootstrap and obtain new universal results on the existence of relevant deformations preserving different amounts of supersymmetry.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

A one-loop test of the near-AdS 2 /near-CFT 1 correspondence

We analyze quantum fluctuations around black hole solutions to the Jackiw-Teitelboim model. We use harmonic analysis on Euclidean AdS 2 to show that the logarithmic corrections to the partition function are determined entirely by quadratic holomorphic differentials, even when conformal symmetry is broken and harmonic modes are no longer true zero modes. Our quantum-corrected partition function agrees precisely with the SYK result. We argue that our effective quantum field theory methods and results generalize to other theories of two-dimensional dilaton gravity.

2D Gravity↗
DOE OSTI2024

Laplace's method applied to functional integrals

In statistical thermodynamics, partition functions are required to evaluate the current state. It is typically impossible to analytically calculate the resulting configuration integrals, but it is sometimes possible to obtain approximations in the limit of steep potential energies. This approach directly leverages Laplace’s method for approximating integrals and has been quite successful in recent applications. Motivated by models with an infinite number of degrees of freedom, this approach should be extended to the statistical thermodynamics of fields. To that end, Laplace’s method is developed for functional integrals.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

BPS spectra and 3-manifold invariants

We provide a physical definition of new homological invariants H a (M 3 ) of 3-manifolds (possibly, with knots) labeled by abelian flat connections. The physical system in question involves a 6d fivebrane theory on M 3 times a 2-disk, D 2 , whose Hilbert space of BPS states plays the role of a basic building block in categorification of various partition functions of 3d N = 2 theory T[M 3 ]: D 2 × S 1 half-index, S 2 × S 1 superconformal index, and S 2 × S 1 topologically twisted index. The first partition function is labeled by a choice of boundary condition and provides a refinement of Chern–Simons (WRT) invariant. A linear combination of them in the unrefined limit gives the analytically continued WRT invariant of M 3 . The last two can be factorized into the product of half-indices. Here, we show how this works explicitly for many examples, including Lens spaces, circle fibrations over Riemann surfaces, and plumbed 3-manifolds.

3-manifold↗
DOE OSTI2024

Universal asymptotics for high energy CFT data

Equilibrium finite temperature observables of a CFT can be described by a local effective action for background fields — a “thermal effective action”. This effective action determines the asymptotic density of states of a CFT as a detailed function of dimension and spin. We discuss subleading perturbative and nonperturbative corrections to the density, comparing with free and holographic examples. We furthermore show how to use the thermal effective action on more complicated geometries at special locations called “hot spots”. The hot spot idea makes a prediction for a CFT partition function on a higher-dimensional version of a genus-2 Riemann surface, in a particular high temperature limit. By decomposing the partition function into a novel higher-dimensional version of genus-2 conformal blocks (which we compute at large scaling dimension), we extract the asymptotic density of heavy-heavy-heavy OPE coefficients in a higher-dimensional CFT. We also compute asymptotics of thermal 1-point functions using the same techniques.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Tests of Seiberg-like dualities in three dimensions

We use localization techniques to study several duality proposals for supersymmetric gauge theories in three dimensions reminiscent of Seiberg duality. We compare the partition functions of dual theories deformed by real mass terms and FI parameters. We find that Seiberg-like duality for N = 3 Chern-Simons gauge theories proposed by Giveon and Kutasov holds on the level of partition functions and is closely related to level-rank duality in pure Chern-Simons theory. We also clarify the relationship between the Giveon-Kutasov duality and a duality in theories of fractional M2 branes and propose a generalization of the latter. Our analysis also confirms previously known results concerning decoupled free sectors in N = 4 gauge theories realized by monopole operators.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2020

Universality driven analytic structure of QCD crossover: radius of convergence and QCD critical point

Recent lattice QCD calculations show strong indications that the crossover of QCD at zero baryon chemical potential (µB) is a remnant of the second order chiral phase transition. The non-universal parameters needed to map temperature T and µ B to the universal properties of the second order chiral phase transition were determined by lattice QCD calculations. Motivated by these advances, first, we discuss the analytic structure of the partition function - the so-called Yang-Lee edge singularity - in the QCD crossover regime, solely based on universal properties. Then, utilizing the lattice calculated non-universal parameters, we map this singularity to the real T and complex µ B plane, in order to find the radius of convergence for a Taylor series expansion of QCD partition function around µ B = 0 in the QCD crossover regime. Our most important findings are: (i) An universality-based estimate of the radius of convergence around µ B = 0; (ii) Universality and lattice QCD based constraints on the location of the QCD critical point in the T - µ B plane.

73 NUCLEAR PHYSICS AND RADIATION PHYSICS↗