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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 19 records
All sourcesNASA NTRSDOE OSTI
DOE OSTI2024

Fermionic shift symmetries in (anti) de Sitter space

We study extended shift symmetries that arise for fermionic fields on anti-de Sitter (AdS) space and de Sitter (dS) space for particular values of the mass relative to the curvature scale. We classify these symmetries for general mixed-symmetry fermionic fields in arbitrary dimension and describe how fields with these symmetries arise as the decoupled longitudinal modes of massive fermions as they approach partially massless points. For the particular case of AdS 4 , we look for non-trivial Lie superalgebras that can underly interacting theories that involve these fields. We study from this perspective the minimal such theory, the Akulov-Volkov theory on AdS 4 , which is a non-linear theory of a spin-1/2 Goldstino field that describes the spontaneous breaking of $\mathcal{N}$ = 1 supersymmetry on AdS 4 down to the isometries of AdS 4 . We show how to write the nonlinear supersymmetry transformation for this theory using the fermionic ambient space formalism. We also study the Lie superalgebras of candidate multi-field examples and rule out the existence of a supersymmetric special galileon on AdS 4 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Non-invertible symmetries in finite-group gauge theory

We investigate the invertible and non-invertible symmetries of topological finite-group gauge theories in general spacetime dimensions, where the gauge group can be abelian or non-abelian. We focus in particular on the 0-form symmetry. The gapped domain walls that generate these symmetries are specified by boundary conditions for the gauge fields on either side of the wall. We investigate the fusion rules of these symmetries and their action on other topological defects including the Wilson lines, magnetic fluxes, and gapped boundaries. We illustrate these constructions with various novel examples, including non-invertible electric-magnetic duality symmetry in 3+1d \mathbb{Z}_2 ℤ 2 gauge theory, and non-invertible analogs of electric-magnetic duality symmetry in non-abelian finite-group gauge theories. In particular, we discover topological domain walls that obey Fibonacci fusion rules in 2+1d gauge theory with dihedral gauge group of order 8. We also generalize the Cheshire string defect to analogous defects of general codimensions and gauge groups and show that they form a closed fusion algebra.

Córdova, Clay↗
DOE OSTI2024

Symmetry-Based Structured Matrices for Efficient Approximately Equivariant Networks

There has been much recent interest in designing symmetry-aware neural networks (NNs) exhibiting relaxed equivariance. Such NNs aim to interpolate between being exactly equivariant and being fully flexible, affording consistent performance benefits. In a separate line of work, certain structured parameter matrices -- those with displacement structure, characterized by low displacement rank (LDR) -- have been used to design small-footprint NNs. Displacement structure enables fast function and gradient evaluation, but permits accurate approximations via compression primarily to classical convolutional neural networks (CNNs). In this work, we propose a general framework -- based on a novel construction of symmetry-based structured matrices -- to build approximately equivariant NNs with significantly reduced parameter counts. Our framework integrates the two aforementioned lines of work via the use of so-called Group Matrices (GMs), a forgotten precursor to the modern notion of regular representations of finite groups. GMs allow the design of structured matrices -- resembling LDR matrices -- which generalize the linear operations of a classical CNN from cyclic groups to general finite groups and their homogeneous spaces. We show that GMs can be employed to extend all the elementary operations of CNNs to general discrete groups. Further, the theory of structured matrices based on GMs provides a generalization of LDR theory focussed on matrices with cyclic structure, providing a tool for implementing approximate equivariance for discrete groups. We test GM-based architectures on a variety of tasks in the presence of relaxed symmetry. We report that our framework consistently performs competitively compared to approximately equivariant NNs, and other structured matrix-based compression frameworks, sometimes with a one or two orders of magnitude lower parameter count.

Samudre, Ashwin↗
DOE OSTI2024

Two loop renormalization of scalar theories using a geometric approach

We derive a general formula for two-loop counterterms in Effective Field Theories (EFTs) using a geometric approach. This formula allows the two-loop results of our previous paper to be applied to a wide range of theories. The two-loop results hold for loop graphs in EFTs where the interaction vertices contain operators of arbitrarily high dimension, but at most two derivatives. We also extend our previous one-loop result to include operators with an arbitrary number of derivatives, as long as there is at most one derivative acting on each field. The final result for the two-loop counterterms is written in terms of geometric quantities such as the Riemann curvature tensor of the scalar manifold and its covariant derivatives. As applications of our results, we give the two-loop counterterms and renormalization group equations for the O(n) EFT to dimension six, the scalar sector of the Standard Model Effective Field Theory (SMEFT) to dimension six, and chiral perturbation theory to order p 6 .

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
NASA NTRS1985

Hopf bifurcation in the presence of symmetry

Group theory is applied to obtain generalized differential equations from the Hopf bifurcation theory on branching to periodic solutions. The conditions under which the symmetry group will admit imaginary eigenvalues are delimited. The action of the symmetry group on the circle group are explored and the Liapunov-Schmidt reduction is used to prove the Hopf theorem in the symmetric case. The emphasis is on simplifying calculations of the stability of bifurcating branches. The resulting general theory is demonstrated in terms of O(2) acting on a plane, O(n) in n-space, and O(3) and an irreducible model for spherical harmonics.

Golubitsky, M.↗
DOE OSTI2024

Non-invertible duality interfaces in field theories with exotic symmetries

In recent years, the concept of global symmetry has generalized considerably. Two dramatic examples of this generalization are the exotic symmetries that govern theories with fractons and non-invertible symmetries, which do not fuse according to a group law. Only recently has the interplay between these two been examined. In this paper, we provide further examples of the interplay in the XY plaquette model, XY cube model, 1+1 d theory with global dipole symmetry, and the 2+1 d Lifshitz theory. They are analogs of the duality symmetries in 2d CTFs and are constructed by first gauging a finite subgroup of the momentum symmetry on half of spacetime and then performing a duality transformation. We analyze the fusion rules of the symmetries and find that they are condensation defects from an analog of higher gauging exotic symmetries. We also address their dependence on the UV cutoff when relevant.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

New procedure for evaluation of U(3) coupling and recoupling coefficients

A simple method to calculate Wigner coupling coefficients and Racah recoupling coefficients for U(3) in two group–subgroup chains is presented. While the canonical U(3) coupling and recoupling coefficients are applicable to any system that respects U(3) symmetry, the U(3) coupling coefficients are more specific to nuclear structure studies. This new procedure precludes the use of binomial coefficients and alternating sums which were used in the 1973 formulation of Draayer and Akiyama, and in so doing provides a faster and more accurate determination of any and all required results. The resolution of the outer multiplicity is based on the null space concept of the U(3) generators proposed by Alex et al., whereas the inner multiplicity in the angular momentum subgroup chain is obtained from the dimension of the null space of the SO(3) raising operator. It is anticipated that a C++ library will ultimately be available for determining generic coupling and recoupling coefficients associated with both the canonical and the physical group–subgroup chains of U(3).

Cross-Coupling Reaction↗
DOE OSTI2024

Coupling and recoupling coefficients for Wigner’s U(4) supermultiplet symmetry

A novel procedure for evaluating Wigner coupling coefficients and Racah recoupling coefficients for U(4) in two group–subgroup chains is presented. The canonical U(4) > U(3) > U(2) > U(1) coupling and recoupling coefficients are applicable to any system that possesses U(4) symmetry, while the physical U(4) coupling coefficients are more specific to nuclear structure studies that utilize Wigner’s supermultiplet symmetry concept. The procedure that is proposed sidesteps the use of binomial coefficients and alternating sum series and consequently enables fast and accurate computation of any and all U(4)-underpinned features. The inner multiplicity of a (S, T) pair within a single U(4) > SU S (2) Ⓧ SU T (2) irreducible representation is obtained from the dimension of the null space of the SU(2) raising generators, while the resolution for the outer multiplicity follows from the work of Alex et al. on U(N) . It is anticipated that a C++ library will ultimately be available for determining generic coupling and recoupling coefficients associated with both the canonical and the physical group–subgroup chains of U(4).

Cross-Coupling Reaction↗
DOE OSTI2025

Spinor representations for fields with any spin: Lorentz tensor basis for operators and covariant multipole decomposition

This paper discusses a framework to parametrize and decompose operator matrix elements for particles with higher spin (j > 1/2) using chiral representations of the Lorentz group, i.e. the (j, 0) and (0, j) representations and their parity-invariant direct sum. Unlike traditional approaches that require imposing constraints to eliminate spurious degrees of freedom, these chiral representations contain exactly the 2j + 1 components needed to describe a spin-j particle. The central objects in the construction are the t-tensors, which are generalizations of the Pauli four-vector σ μ for higher spin. For the generalized spinors of these representations, we demonstrate how the algebra of the t-tensors allows to formulate a generalization of the Dirac matrix basis for any spin. For on-shell bilinears, we show that a set consisting exclusively of covariant multipoles of order 0 ≤ m ≤ 2j forms a complete basis. We provide explicit expressions for all bilinears of the generalized Dirac matrix basis, which are valid for any spin value. As a byproduct of our derivations we present an efficient algorithm to compute the t-tensor matrix elements. The formalism presented here paves the way to use a more unified approach to analyze the non-perturbative QCD structure of hadrons and nuclei across different spin values, with clear physical interpretation of the resulting distributions as covariant multipoles.

Angular momentum of light↗
DOE OSTI2024

On amplitudes and field redefinitions

We derive an off-shell recursion relation for correlators that holds at all loop orders. This allows us to prove how generalized amplitudes transform under generic field redefinitions, starting from an assumed behavior of the one-particle-irreducible effective action. The form of the recursion relation resembles the operation of raising the rank of a tensor by acting with a covariant derivative. This inspires a geometric interpretation, whose features and flaws we investigate.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2025

Rational QCD loop amplitudes and quantum theories on twistor space

We show how curing an anomaly of the twistor uplift of self-dual Yang-Mills theory implies linear relations among one-loop, n-gluon, color-ordered subamplitudes in QCD, when all n gluon helicities are positive, or when exactly one is negative. We compute the number of linearly independent subamplitudes as determined by these relations, in terms of unsigned Stirling numbers. Then we use a momentum-twistor parametrization to show that there are no further linear dependencies.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Hilbert series for covariants and their applications to minimal flavor violation

We elaborate how to apply the Hilbert series method to enumerating group covariants, which transform under any given representation, including but going beyond group invariants. Mathematically, group covariants form a module over the ring of the invariants. The number of independent covariants is given by the rank of the module, which can be computed by taking a ratio of two Hilbert series. In many cases, the rank equals the dimension of the group covariant representation. When this happens, we say that there is a rank saturation. We apply this technology to revisit the hypothesis of Minimal Flavor Violation in constructing Effective Field Theories beyond the Standard Model. We find that rank saturation is guaranteed in this case, leading to the important consequence that the MFV symmetry principle does not impose any restriction on the EFT, i.e. MFV SMEFT = SMEFT, in the absence of additional assumptions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2022

Algebraic Theory of Patterns as Generalized Symmetries

We generalize the exact predictive regularity of symmetry groups to give an algebraic theory of patterns, building from a core principle of future equivalence. For topological patterns in fully-discrete one-dimensional systems, future equivalence uniquely specifies a minimal semiautomaton. We demonstrate how the latter and its semigroup algebra generalizes translation symmetry to partial and hidden symmetries. This generalization is not as straightforward as previously considered. Here, though, we clarify the underlying challenges. A stochastic form of future equivalence, known as predictive equivalence, captures distinct statistical patterns supported on topological patterns. Finally, we show how local versions of future equivalence can be used to capture patterns in spacetime. As common when moving to higher dimensions, there is not a unique local approach, and we detail two local representations that capture different aspects of spacetime patterns. A previously developed local spacetime variant of future equivalence captures patterns as generalized symmetries in higher dimensions, but we show that this representation is not a faithful generator of its spacetime patterns. This motivates us to introduce a local representation that is a faithful generator, but we demonstrate that it no longer captures generalized spacetime symmetries. Taken altogether, building on future equivalence, the theory defines and quantifies patterns present in a wide range of classical field theories.

97 MATHEMATICS AND COMPUTING↗
DOE OSTI2020

Generic Construction of the Standard Model Gauge Group and Matter Representations in F-theory

In this work, we describe general classes of 6D and 4D F-theory models with gauge group (SU(3)×SU(2)×U(1))/Z 6 . For 6D F-theory models with no tensor multiplets, we prove that this set of constructions gives all possible consistent supergravity theories with this gauge group and the corresponding generic matter representations, which include those of the MSSM. We expect, though do not prove, that these models are similarly generic for 6D theories with tensor multiplets and for 4D N=1 supergravity theories. Finally, the models in the largest class of these constructions come from deforming an underlying geometry with SU(4)×SU(3)×SU(2), corresponding to Higgsing on three bifundamental fields.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2023

An algebraic formula for two loop renormalization of scalar quantum field theory

We find a general formula for the two-loop renormalization counterterms of a scalar quantum field theory with interactions containing up to two derivatives, extending ’t Hooft’s one-loop result. The method can also be used for theories with higher derivative interactions, as long as the terms in the Lagrangian have at most one derivative acting on each field. We show that diagrams with factorizable topologies do not contribute to the renormalization group equations. The results in this paper will be combined with the geometric method in a subsequent paper to obtain the counterterms and renormalization group equations for the scalar sector of effective field theories (EFT) to two-loop order.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

ADG: automated generation and evaluation of many-body diagrams

The goal of the present paper is twofold. First, a novel expansion many-body method applicable to superfluid open-shell nuclei, the so-called Bogoliubov in-medium similarity renormalization group (BIMSRG) theory, is formulated. This generalization of standard single-reference IMSRG theory for closed-shell systems parallels the recent extensions of coupled cluster, self-consistent Green’s function or many-body perturbation theory. Within the realm of IMSRG theories, BIMSRG provides an interesting alternative to the already existing multi-reference IMSRG (MR-IMSRG) method applicable to open-shell nuclei. The algebraic equations for low-order approximations, i.e., BIMSRG(1) and BIMSRG(2), can be derived manually without much difficulty. However, such a methodology becomes already impractical and error prone for the derivation of the BIMSRG(3) equations, which are eventually needed to reach high accuracy. Based on a diagrammatic formulation of BIMSRG theory, the second objective of the present paper is thus to describe the third version (v3.0) of the code that automatically (1) generates all valid BIMSRG(n) diagrams and (2) evaluates their algebraic expressions in a matter of seconds. This is achieved in such a way that equations can easily be retrieved for both the flow equation and the Magnus expansion formulations of BIMSRG. Expanding on this work, the first future objective is to numerically implement BIMSRG(2) (eventually BIMSRG(3)) equations and perform ab initio calculations of mid-mass open-shell nuclei.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Bounding entanglement entropy with Clifford double cosets

Following on our previous work studying the orbits of quantum states under Clifford circuits via reachability graphs, we introduce contracted graphs whose vertices represent classes of quantum states with the same entropy vector. These contracted graphs represent the double cosets of the Clifford group, where the left cosets are built from the stabilizer subgroup of the starting state and the right cosets are built from the entropy-preserving operators. We study contracted graphs for stabilizer states, as well as 𝑊 states and Dicke states, discussing how the diameter of a state's contracted graph constrains the entropic diversity of its two-qubit Clifford orbit. We derive an upper bound on the number of entropy vectors that can be generated using any 𝑛-qubit Clifford circuit, for any quantum state. Here, we speculate on the holographic implications for the relative proximity of gravitational duals of states within the same Clifford orbit. Although we concentrate on how entropy evolves under the Clifford group, our double-coset formalism, and thus the contracted graph picture, is extendable to generic gate sets and generic state properties.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗