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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 163 records · Page 9
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DOE OSTI2021

Proving the 6d Cardy formula and matching global gravitational anomalies

A Cardy formula for 6d superconformal field theories (SCFTs) conjectured by Di Pietro and Komargodski in [1] governs the universal behavior of the supersymmetric partition function on S^1_\beta \times S^5 S β 1 × S 5 in the limit of small \beta β and fixed squashing of the S^5 S 5 . For a general 6d SCFT, we study its 5d effective action, which is dominated by the supersymmetric completions of perturbatively gauge-invariant Chern-Simons terms in the small \beta β limit. Explicitly evaluating these supersymmetric completions gives the precise squashing dependence in the Cardy formula. For SCFTs with a pure Higgs branch (also known as very Higgsable SCFTs), we determine the Chern-Simons levels by explicitly going onto the Higgs branch and integrating out the Kaluza-Klein modes of the 6d fields on S^1_\beta S β 1 . We then discuss tensor branch flows, where an apparent mismatch between the formula in [1] and the free field answer requires an additional contribution from BPS strings. This ``missing contribution’’ is further sharpened by the relation between the fractional part of the Chern-Simons levels and the (mixed) global gravitational anomalies of the 6d SCFT. We also comment on the Cardy formula for 4d \mathcal{N}=2 𝒩 = 2 SCFTs in relation to Higgs branch and Coulomb branch flows.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

A microscopic realization of dS$_3$

We propose a precise duality between pure de Sitter quantum gravity in 2+1 2 + 1 dimensions and a double-scaled matrix integral. This duality unfolds in two distinct aspects. First, by carefully quantizing the gravitational phase space, we arrive at a novel proposal for the quantum state of the universe at future infinity. We compute cosmological correlators of massive particles in the universe specified by this wavefunction. Integrating these correlators over the metric at future infinity yields gauge-invariant observables, which are identified with the string amplitudes of the complex Liouville string [S. Collier et al., arXiv: 2409.17246]. This establishes a direct connection between integrated cosmological correlators and the resolvents of the matrix integral dual to the complex Liouville string, thereby demonstrating one aspect of the dS _3 3 /matrix integral duality. The second aspect concerns the cosmological horizon of the dS static patch and the Gibbons-Hawking entropy it is conjectured to encode. We show that this entropy can be reproduced exactly by counting the entries of the matrix.

Collier, Scott (ORCID:0000000286476653)↗
DOE OSTI2022

Applying machine learning methods to prediction problems of lattice observables

We discuss the prediction of critical behavior of lattice observables in SU(2) and SU(3) gauge theories. We show that feed-forward neural network, trained on the lattice configurations of gauge fields as input data, finds correlations with the target observable, which is also true in the critical region where the neural network has not been trained. We have verified that the neural network constructs a gauge-invariant function and this property does not change over the entire range of the parameter space.

Gerasimeniuk, Nikolai↗
DOE OSTI2025

Quarkonium Polarization Kinetic Equation from Open Quantum Systems and Effective Field Theories

Recent measurements of polarization phenomena in relativistic heavy ion collisions have aroused a great interest in understanding dynamical spin evolution of the QCD matter. In particular, the spin alignment signature of J/ψ has been recently observed in Pb-Pb collisions at LHC, which may infer nontrivial spin transport of quarkonia in quark gluon plasmas. Motivated by this, we study the spin-dependent in-medium dynamics of quarkonia by using the potential nonrelativistic QCD (pNRQCD) and the open quantum system framework. By applying the Markovian approximation and Wigner transformation, we systematically derive the Boltzmann transport equation for vector quarkonia with polarization dependence in the quantum optical limit. As opposed to the previous study for the spin-independent case where the collision terms depend on chromoelectric correlators, the new kinetic equation incorporates gauge invariant correlators of chromomagnetic fields that determine the recombination and dissociation terms with polarization dependence at the order we are working in the multipole expansion. In the quantum Brownian motion limit, the Lindblad equation with new transport coefficients defined in terms of the chromomagnetic field correlators have also been derived. Our formalism is generic and valid for both weakly-coupled and strongly-coupled quark gluon plasmas. It may be further applied to study spin alignment of vector quarkonia in heavy ion collisions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

The Classical Equations of Motion of Quantized Gauge Theories, Part I: General Relativity

In this and a companion paper, we show that quantum field theories with gauge symmetries permit a broader class of classical dynamics than typically assumed. In this article, we show that the dynamics extracted from the path integral or Hamiltonian formulation of general relativity allows for classical states that do not satisfy the full set of Einstein's equations. This amounts to loosening the Hamiltonian and momentum constraints that are imposed on the initial state. Nevertheless, the quantum theory permits gauge invariant time evolution of these states. The time evolution of these states is such that at the classical level the full set of Einstein's equations would appear to hold, with the physical effects of these states being attributable to an auxiliary, covariantly conserved energy-momentum tensor with no internal degrees of freedom. We derive the generalized Einstein equations for these states and show that a homogeneous and isotropic initial background state contributes to expansion identical to cold dark matter. The inhomogeneous components of this state could source curvature perturbations that grow linearly at linear order. This auxiliary contribution to Einstein's equations could have either sign and thus provide a trivial way to violate the null energy condition, enabling novel gravitational dynamics such as cosmic bounces and wormholes.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Revisiting Gauge Ambiguities for DUNE Precision

The de Forest prescription for handling off-shell initial states in the impulse approximation for lepton-nucleus scattering breaks gauge invariance. We discuss existing methods to address this problem and handle the form factor scale ambiguity. We demonstrate that the irreducible differences between the prescriptions are significant compared to the precision expected of next-generation accelerator neutrino experiments. A novel approach directly using the off-shell currents is proposed as a systematically improvable alternative.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2026

A Space-Time Fluid (Unabridged)

Purpose: This essay is a retelling of general relativity in a language in which space-time geometry is expressed as a fluid. This trivial and useful reformulation gives 1) a non-perturbative covariant description of cosmological inhomogeneities and 2) a simple formula describing how cosmic inhomogeneities are generated on super-horizon scales. Methods: Equating the Ricci curvature with the associated matter stress-energy gives a description of space-time geometry in terms of fluid properties. These locally measurable (covariant) non-perturbative quantities are in some ways superior to commonly used "gauge invariant" quantities. The dynamics of a quantity (kurvature) which describes cosmological inhomogeneities is described in detail. A detailed comparison is made of space-time fluid dynamics with that of a classical (Newtonian physics) fluid. Results: The fluid lexicon permits an unambiguous definition of the velocity of space-time. The evolution of the space-time fluid is in many ways identical with that of the classical fluid when expressed in Lagrangian coordinates. Kurvature is a measure of the specific binding energy of the fluid and is a most useful covariant measure of cosmological inhomogeneities. For plausible matter models kurvature will increase, even on super-horizon scales, due to non-linear hydrodynamic effects rather than gravity. This phenomena is also exhibited by classical fluids. Conclusion: The space-time fluid representation of geometrodynamics gives a simple and useful description of the evolution of cosmological inhomogeneities.

Stebbins, Albert [Fermilab] (ORCID:000000023807725↗
DOE OSTI2024

The Gauge Picture of Quantum Dynamics

Although local Hamiltonians exhibit local time dynamics, this locality is not explicit in the Schrödinger picture in the sense that the wavefunction amplitudes do not obey a local equation of motion. We show that geometric locality can be achieved explicitly in the equations of motion by "gauging" the global unitary invariance of quantum mechanics into a local gauge invariance. That is, expectation values $\langle \psi|A|\psi \rangle$ are invariant under a global unitary transformation acting on the wavefunction $|\psi\rangle \to U |\psi\rangle$ and operators $A \to U A U^\dagger$, and we show that it is possible to gauge this global invariance into a local gauge invariance. To do this, we replace the wavefunction with a collection of local wavefunctions $|\psi_J\rangle$, one for each patch of space $J$. The collection of spatial patches is chosen to cover the space; e.g. we could choose the patches to be single qubits or nearest-neighbor sites on a lattice. Local wavefunctions associated with neighboring pairs of spatial patches $I$ and $J$ are related to each other by dynamical unitary transformations $U_{IJ}$. The local wavefunctions are local in the sense that their dynamics are local. That is, the equations of motion for the local wavefunctions $|\psi_J\rangle$ and connections $U_{IJ}$ are explicitly local in space and only depend on nearby Hamiltonian terms. (The local wavefunctions are many-body wavefunctions and have the same Hilbert space dimension as the usual wavefunction.) We call this picture of quantum dynamics the gauge picture since it exhibits a local gauge invariance. The local dynamics of a single spatial patch is related to the interaction picture, where the interaction Hamiltonian consists of only nearby Hamiltonian terms. We can also generalize the explicit locality to include locality in local charge and energy densities.

Physics↗
DOE OSTI2024

Self-duality under gauging a non-invertible symmetry

Abstract We discuss two-dimensional conformal field theories (CFTs) which are invariant under gauging a non-invertible global symmetry. At every point on the orbifold branch ofc= 1 CFTs, it is known that the theory is self-dual under gauging a ℤ 2 × ℤ 2 symmetry, and has Rep(H 8 ) and Rep(D 8 ) fusion category symmetries as a result. We find that gauging the entire Rep(H 8 ) fusion category symmetry maps the orbifold theory at radiusRto that at radius 2/R. AtR=$$ \sqrt{2} $$ 2 , which corresponds to two decoupled Ising CFTs (Ising 2 in short), the theory is self-dual under gauging the Rep(H 8 ) symmetry. This implies the existence of a topological defect line in the Ising 2 CFT obtained from half-space gauging of the Rep(H 8 ) symmetry, which commutes with thec= 1 Virasoro algebra but does not preserve the fully extended chiral algebra. We bootstrap its action on thec= 1 Virasoro primary operators, and find that there are no relevant or marginal operators preserving it. Mathematically, the new topological line combines with the Rep(H 8 ) symmetry to form a bigger fusion category which is a ℤ 2 -extension of Rep(H 8 ). We solve the pentagon equations including the additional topological line and find 8 solutions, where two of them are realized in the Ising 2 CFT. Finally, we show that the torus partition functions of the Monster 2 CFT and Ising×Monster CFT are also invariant under gauging the Rep(H 8 ) symmetry.

Physics↗
DOE OSTI2021

Lorentz invariance of basis tensor gauge theory

Basis tensor gauge theory (BTGT) is a vierbein analog reformulation of ordinary gauge theories in which the vierbein field describes the Wilson line. After a brief review of the BTGT, we clarify the Lorentz group representation properties associated with the variables used for its quantization. In particular, we show that starting from an SO(1,3) representation satisfying the Lorentz-invariant U(1,3) matrix constraints, BTGT introduces a Lorentz frame choice to pick the Abelian group manifold generated by the Cartan subalgebra of U(1,3) for the convenience of quantization even though the theory is frame independent. This freedom to choose a frame can be viewed as an additional symmetry of BTGT that was not emphasized before. We then show how an [Formula: see text] permutation symmetry and a parity symmetry of frame fields natural in BTGT can be used to construct renormalizable gauge theories that introduce frame-dependent fields but remain frame independent perturbatively without any explicit reference to the usual gauge field.

Physics↗
DOE OSTI2023

Obstructions to gapped phases from noninvertible symmetries

Quantum systems in 3+1 dimensions that are invariant under gauging a one-form symmetry enjoy novel noninvertible duality symmetries encoded by topological defects. These symmetries are renormalization group invariants which constrain dynamics. We show that such noninvertible symmetries often forbid a symmetry-preserving vacuum state with a gapped spectrum. In particular, we prove that a self-dual theory with $\mathbb{Z}^{(1)}_N$ one-form symmetry is gapless or spontaneously breaks the self-duality symmetry unless N = k 2 ⁢ℓ where –1 is a quadratic residue modulo . We also extend these results to noninvertible symmetries arising from invariance under more general gauging operations including, e.g., triality symmetries. Along the way, we discover how duality defects in symmetry-protected topological phases have a hidden time-reversal symmetry that organizes their basic properties. These noninvertible symmetries are realized in lattice gauge theories, which serve to illustrate our results.

75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND↗
DOE OSTI2021

Higher-rank tensor field theory of non-abelian fracton and embeddon

We formulate a new class of tensor gauge field theories in any dimension that is a hybrid class between symmetric higher-rank tensor gauge theory (i.e., higher-spin gauge theory) and anti-symmetric tensor topological field theory. Our theory describes a mixed unitary phase interplaying between gapless and gapped topological order phases (which can live with or without Euclidean, Poincaré, or anisotropic symmetry, at least in ultraviolet high or intermediate energy field theory, but not yet to a lattice cutoff scale). The “gauge structure” can be compact, continuous, abelian or non-abelian. Our theory sits outside the paradigm of Maxwell electromagnetic theory in 1865 and Yang–Mills isospin/color theory in 1954. We discuss its local gauge transformation in terms of the ungauged vector-like or tensor-like higher-moment global symmetry. The non-abelian gauge structure is caused by gauging the non-commutative symmetries: a higher-moment symmetry and a charge conjugation (particle–hole) symmetry. Vector global symmetries along time direction may exhibit time crystals. We explore the relation of these long-range entangled matters to a non-abelian generalization of Fracton order in condensed matter, a field theory formulation of foliation, the spacetime embedding and Embeddon that we newly introduce, and possible fundamental physics applications to dark matter or dark energy.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Algebraic Structures in the Coupling of Gravity to Gauge Theories

Highlights: • Geometric foundation for Quantum General Relativity coupled to Quantum Electrodynamics. • Rigorous introduction to Hopf algebraic renormalization. • Appropriate modifications in case renormalization Hopf algebra is ill-defined. • Generalization of Furry’s Theorem to include gravitons and ghosts. • Discussion of obstructions to multiplicative renormalization. This article is an extension of the author’s second master thesis, Prinz (2017). It aims to introduce to the theory of perturbatively quantized General Relativity coupled to Spinor Electrodynamics, provide the results thereof and set the notation to serve as a starting point for further research in this direction. It includes the differential geometric and Hopf algebraic background, as well as the corresponding Lagrange density and some renormalization theory. Then, a particular problem in the renormalization of Quantum General Relativity coupled to Quantum Electrodynamics is addressed and solved by a generalization of Furry’s Theorem. Next, the restricted combinatorial Green’s functions for all two-loop propagators and all one-loop divergent subgraphs thereof are presented. Finally, relations between these one-loop restricted combinatorial Green’s functions necessary for multiplicative renormalization are discussed.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

On restricting first order form of gauge theories to one-loop order

Highlights: • We prove the equivalence of the first and second-order formalism. • We use Lagrange multiplier fields to limit radiative effects to one-loop order. • We prove that the quantized theory is both renormalizable and unitary. The first order form of the Yang–Mills and Einstein–Hilbert actions are quantized, and it is shown how Green’s functions computed using the first and the second order form of these theories are related. Next we show how by use of Lagrange multiplier fields (LM), radiative effects beyond one-loop order can be eliminated. This allows one to compute Green’s functions exactly without loss of unitarity. The consequences of this restriction on radiative effects are examined for the Yang–Mills and Einstein–Hilbert actions. In these two gauge theories, we find that the quantized theory is both renormalizable and unitary once the LM field is used to eliminate effects beyond one-loop order.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Fractonic gauge theory of smectics

Motivated by striped correlated quantum matter, and the recently developed duality between elasticity of a two-dimensional (2D) crystal and a gauge theory, we derive a dual coupled U(1) vector gauge theory for a two-dimensional (2D) quantum smectic, where the disclination is mapped onto the fractonic charge, that we demonstrate can only move transversely to smectic layers. This smectic gauge theory dual also emerges from a gauge dual of a quantum crystal through a Higgs transition corresponding to a single flavor of its dipole condensation, an anisotropic quantum melting via dislocation proliferation. A condensation of the second flavor of dislocations a corresponds to another Higgs transition describing the smectic-to-nematic melting. We also utilize the electrostatic limit of this duality to formulate a melting of a 2D classical smectic in terms of a higher derivative sine–Gordon model, demonstrating its instability to a nematic at any nonzero temperature. Generalizing this classical duality to a 3D smectic, gives formulation of a 3D nematic-to-smectic transition in terms of an anisotropic Abelian-Higgs model.

36 MATERIALS SCIENCE↗
DOE OSTI2021

Restricting loop expansions in gauge theories coupled to matter

Highlights: • Lagrange multiplier fields are used to restrict radiative effects to one-loop order. • This approach is exemplified in the Yang-Mills theory coupled to a scalar matter field. • We showed that it can be used with the Einstein–Hilbert action coupled to matter. • The resulting quantum gravity theory is both renormalizable and unitary. Quantizing any model in which a Lagrange multiplier (LM) field is used to restrict field configurations to those that satisfy the classical equations of motion, leads to at most one-loop radiative corrections. This approach can be used with both the Yang–Mills (YM) and Einstein–Hilbert (EH) action; the resulting theory is both renormalizable and unitary, has a positive energy spectrum and has no negative norm states contributing to physical processes. Although this approach cannot be consistently used with scalar fields alone, scalar fields can be coupled to gauge fields so that loop effects in the gauge sector are restricted to one-loop order in a way that satisfies the usual criterion for a consistent quantum field theory. The tree-level diagrams are those of the classical theory in which the metric couples to the energy–momentum tensor.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗