Engineering Papers⌕ Search

SEARCH · Engineering Papers

Results for “Gauge group”

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.

Quote a phrase for an exact phrase match. Source license links do not imply unrestricted reuse.

At least 37 records · Page 2
All sourcesNASA NTRSDOE OSTI
DOE OSTI2025

Finite-temperature phase diagram of the Berenstein-Maldacena-Nastase matrix model on the lattice

We investigate the thermal phase structure of the Berenstein-Maldacena-Nastase matrix model using nonperturbative lattice Monte Carlo calculations. Our main analyses span 3 orders of magnitude in the coupling, involving systems with sizes up to 𝑁𝜏 =24 lattice sites and SU⁡(𝑁) gauge groups with 8 ≤𝑁 ≤16. In addition, we carry out extended checks of discretization artifacts for 𝑁𝜏 ≤128 and gauge group SU(4). We find results for the deconfinement temperature that interpolate between the perturbative prediction at weak coupling and the large-𝑁 dual supergravity calculation at strong coupling. While we confirm that the phase transition is first order for strong coupling, it appears to be continuous for weaker couplings.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

More about the lattice Hamiltonian for Adjoint QCD 2

In our earlier work [1], we introduced a lattice Hamiltonian for Adjoint QCD 2 using staggered Majorana fermions. We found the gauge invariant space of states explicitly for the gauge group SU(2) and used them for numerical calculations of observables, such as the spectrum and the expectation value of the fermion bilinear. In this paper, we carry out a more in-depth study of our lattice model, extending it to any compact and simply-connected gauge group G. We show how to find the gauge invariant space of states and use it to study various observables. We also use the lattice model to calculate the mixed ’t Hooft anomalies of Adjoint QCD 2 for arbitrary G. We show that the matrix elements of the lattice Hamiltonian can be expressed in terms of the Wigner 6j-symbols of G. For G = SU(3), we perform exact diagonalization for lattices of up to six sites and study the low-lying spectrum, the fermion bilinear condensate, and the string tension. We also show how to write the lattice strong coupling expansion for ground state energies and operator expectation values in terms of the Wigner 6j-symbols. For SU(3) we carry this out explicitly and find good agreement with the exact diagonalizations, and for SU(4) we give expansions that can be compared with future numerical studies.

confinement↗
DOE OSTI2025

Composite quarks and leptons with embedded QCD

We construct a model of quark and lepton compositeness based on an 𝑆⁢𝑈⁡(15) gauge interaction that confines chiral preons, which are also charged under the weakly coupled 𝑆⁢𝑈⁢(4) PS ×𝑆⁢𝑈⁢(2) 𝐿 ×𝑆⁢𝑈⁢(2) 𝑅 gauge group. The breaking of the latter, down to the Standard Model group, is achieved by scalar 𝑆⁢𝑈⁡(15) bound states at a scale in the 30–100 TeV range. The embedding of the QCD gauge group in 𝑆⁢𝑈⁢(4) PS slows down the running of 𝛼 𝑠 in the UV. We estimate the effects of the strongly coupled 𝑆⁢𝑈⁡(15) dynamics on the running of the 𝑆⁢𝑈⁢(4) PS ×𝑆⁢𝑈⁢(2) 𝐿 ×𝑆⁢𝑈⁢(2) 𝑅 gauge couplings, which likely remain perturbative beyond the compositeness scale of about 10 3 –10 4 TeV, and even above a unification scale. A composite vectorlike lepton doublet acquires a mass in the TeV range probed at future colliders, and an extended Higgs sector arises from six-preon bound states.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Axion domain walls, small instantons, and non-invertible symmetry breaking

Non-invertible global symmetry often predicts degeneracy in axion potentials and carries important information about the global form of the gauge group. When these symmetries are spontaneously broken they can lead to the formation of stable axion domain wall networks which support topological degrees of freedom on their worldvolume. Such non-invertible symmetries can be broken by embedding into appropriate larger UV gauge groups where small instanton contributions lift the vacuum degeneracy, and provide a possible solution to the domain wall problem. We explain these ideas in simple illustrative examples and then apply them to the Standard Model, whose gauge algebra and matter content are consistent with several possible global structures. Each possible global structure leads to different selection rules on the axion couplings, and various UV completions of the Standard Model lead to more specific relations. As a proof of principle, we also present an example of a UV embedding of the Standard Model which can solve the axion domain wall problem. The formation and annihilation of the long-lived axion domain walls can lead to observables, such as gravitational wave signals. Observing such signals, in combination with the axion coupling measurements, can provide valuable insight into the global structure of the Standard Model, as well as its UV completion.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

General F-theory models with tuned (SU(3) × SU(2) × U(1))/ Z 6 symmetry

We construct a general form for an F-theory Weierstrass model over a general base giving a 6D or 4D supergravity theory with gauge group (SU(3) × SU(2) × U(1))/Z 6 and generic associated matter, which includes the matter content of the standard model. The Weierstrass model is identified by unHiggsing a model with U(1) gauge symmetry and charges q ≤ 4 previously found by the first author. This model includes two distinct branches that were identified in earlier work, and includes as a special case the class of models recently studied by Cvetič, Halverson, Lin, Liu, and Tian, for which we demonstrate explicitly the possibility of unification through an SU(5) unHiggsing. We develop a systematic methodology for checking that a parameterized class of F-theory Weierstrass models with a given gauge group G and fixed matter content is generic (contains all allowed moduli) and confirm that this holds for the models constructed here.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Majorana fermion dark matter in minimally extended left-right symmetric model

We present a minimal extension of the left-right symmetric model based on the gauge group SU(3) c × SU(2) L × SU(2) R × U(1) B–L × U(1) X , in which a vector-like fermion pair ( ζ L and ζ R ) charged under the U(1) B–L × U(1) X symmetry is introduced. Associated with the symmetry breaking of the gauge group SU(2) R × U(1) B–L × U(1) X down to the Standard Model (SM) hypercharge U(1) Y , Majorana masses for ζ L,R are generated and the lightest mass eigenstate plays a role of the dark matter (DM) in our universe by its communication with the SM particles through a new neutral gauge boson “ X ”. We consider various phenomenological constraints of this DM scenario, such as the observed DM relic density, the LHC Run-2 constraints from the search for a narrow resonance, and the perturbativity of the gauge couplings below the Planck scale. Combining all constraints, we identify the allowed parameter region which turns out to be very narrow. A significant portion of the currently allowed parameter region will be tested by the High-Luminosity LHC experiments.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2025

Cascading from $\mathscr{N}$ = 2 supersymmetric Yang–Mills theory to confinement and chiral symmetry breaking in adjoint QCD

We argue that adjoint QCD in 3 + 1 dimensions, with any SU(N) gauge group and two Weyl fermion flavors (i.e. one adjoint Dirac fermion), confines and spontaneously breaks its chiral symmetries via the condensation of a fermion bilinear. We flow to this theory from pure $\mathscr{N}$ = 2 SUSY Yang–Mills theory with the same gauge group, by giving a SUSY-breaking mass M to the scalars in the $\mathscr{N}$ = 2 vector multiplet. This flow can be analyzed rigorously at small M, where it leads to a deconfined vacuum at the origin of the $\mathscr{N}$ = 2 Coulomb branch. The analysis can be extended to all M using an Abelian dual description that arises from the N multi-monopole points of the $\mathscr{N}$ = 2 theory. At each such point, there are N −1 hypermultiplet Higgs fields h$^{i=1,2}_m$, which are SU(2) R doublets. We provide a detailed study of the phase diagram as a function of M, by analyzing the semi-classical phases of the dual using a combination of analytic and numerical techniques. The result is a cascade of first-order phase transitions, along which the Higgs fields h i m successively turn on, and which interpolates between the Coulomb branch at small M, where all h$^{i}_m$ = 0, and a maximal Higgs branch, where all h$^{i}_m$ ≠ 0, at sufficiently large M. We show that this maximal Higgs branch precisely matches the confining and chiral symmetry breaking phase of two-flavor adjoint QCD, including its broken and unbroken symmetries, its massless spectrum, and the expected large-N scaling of various observables. The spontaneous breaking pattern SU(2) R → U(1) R , consistent with the Vafa–Witten theorem, is ensured by an intricate alignment mechanism for the h$^{i}_m$ in the dual, and leads to a CP 1 sigma model of increasing radius along the cascade.

D’Hoker, Eric [Univ. of California, Los Angeles, C↗
DOE OSTI2021

Mocking the u-plane integral

Abstract The u -plane integral is the contribution of the Coulomb branch to correlation functions of $${\mathcal {N}}=2$$ N = 2 gauge theory on a compact four-manifold. We consider the u -plane integral for correlators of point and surface observables of topologically twisted theories with gauge group $$\mathrm{SU}(2)$$ SU ( 2 ) , for an arbitrary four-manifold with $$(b_1,b_2^+)=(0,1)$$ ( b 1 , b 2 + ) = ( 0 , 1 ) . The u -plane contribution equals the full correlator in the absence of Seiberg–Witten contributions at strong coupling, and coincides with the mathematically defined Donaldson invariants in such cases. We demonstrate that the u -plane correlators are efficiently determined using mock modular forms for point observables, and Appell–Lerch sums for surface observables. We use these results to discuss the asymptotic behavior of correlators as function of the number of observables. Our findings suggest that the vev of exponentiated point and surface observables is an entire function of the fugacities.

Mathematics↗
DOE OSTI2022

Dark matter effective field theory and an application to vector dark matter

The Standard Model Effective Field Theory (SMEFT) and the Low Energy Effective Field Theory (LEFT) can be extended by adding additional spin 0, 1/2 and 1 dark matter particles which are singlets under the Standard Model (SM) gauge group. We classify all gauge invariant interactions in the Lagrangian up to terms of dimension six, and present the tree-level matching conditions between the two theories at the electroweak scale. The most widely studied dark matter models, such as those based on the Higgs portal or on kinetic mixing between the photon and a dark photon, are based on dimension-four interactions with the SM sector. We consider a model with dark vector particles with a $\mathbb{Z}_2$ symmetry, so that the lightest dark matter particle is stable. The leading interaction with the SM is through dimension-six operators involving two dark vector field-strength tensors and the electromagnetic field-strength tensor. This model is a viable dark matter model in the freeze-in scenario for a wide range of parameters.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2021

Charge completeness and the massless charge lattice in F-theory models of supergravity

We prove that, for every 6D supergravity theory that has an F-theory description, the property of charge completeness for the connected component of the gauge group (meaning that all charges in the corresponding charge lattice are realized by massive or massless states in the theory) is equivalent to a standard assumption made in F-theory for how geometry encodes the global gauge theory by means of the Mordell-Weil group of the elliptic fibration. This result also holds in 4D F-theory constructions for the parts of the gauge group that come from sections and from 7-branes. We find that in many 6D F-theory models the full charge lattice of the theory is generated by massless charged states; this occurs for each gauge factor where the associated anomaly coefficient satisfies a simple positivity condition. We describe many of the cases where this massless charge sufficiency condition holds, as well as exceptions where the positivity condition fails, and analyze the related global structure of the gauge group and associated Mordell-Weil torsion in explicit F-theory models.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2021

Sparticle spectroscopy and dark matter in a U(1) B-L extension of MSSM

We consider a class of SUSY models in which the MSSM gauge group is supplemented with a gauged U(1) B-L symmetry and a global U(1) R symmetry. This extension introduces only electrically neutral states, and the new SUSY partners effectively double the number of states in the neutralino sector that now includes a blino (from B - L) and singlino from a gauge singlet superfield. If the DM density is saturated by a LSP neutralino, the model yields quite a rich phenomenology depending on the DM composition. The LSP relic density constraint provides a lower bound on the stop and gluino masses of about 3 TeV and 4 TeV respectively, which is testable in the near future collider experiments such as HL-LHC.

71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSIC↗
DOE OSTI2022

Muonic force behind flavor anomalies

We develop an economical theoretical framework for combined explanations of the flavor physics anomalies involving muons: (g - 2) μ , R K(*), and b → sμ + μ - angular distributions and branching ratios, that was first initiated by some of us in ref. [1]. The Standard Model (SM) is supplemented with a lepton-flavored U(1) X gauge group. The U(1) X gauge boson with the mass of O(0.1) GeV resolves the (g - 2) μ tension. A TeV-scale leptoquark, charged under the U(1) X , carries a muon number and mediates B-decays without prompting charged lepton flavor violation or inducing proton decay. We explore the theory space of the chiral, anomaly-free U(1) X gauge extensions featuring the above scenario, and identify many suitable charge assignments for the SM+3ν R fermion content with the integer charges in the range X F i $\in$ [-10, 10]. We then carry out a comprehensive phenomenological study of the muonic force in representative benchmark models. Interestingly, we found models which can resolve the tension without conflicting the complementary constraints, and all of the viable parameter space will be tested in future muonic resonance searches. Finally, the catalog of the anomaly-free lepton-non-universal charge assignments motivated us to explore different directions in model building. We present a model in which the muon mass and the (g - 2) μ are generated radiatively from a common short-distance dynamics after the U(1) X breaking. We also show how to charge a vector leptoquark under U(1) μ-τ in a complete gauge model.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2024

Towards UV-Models of Kinetic Mixing and Portal Matter VII: A Light Dark Photon in the 3c3L1A1B Model

The kinetic mixing (KM) portal, by which the Standard Model (SM) photon mixes with a light dark photon arising from a new U(1)DU(1)D​ gauge group, allows for the possibility of viable scenarios of sub-GeV thermal dark matter (DM) with appropriately suppressed couplings to the SM. This KM can only occur if particles having both SM and dark quantum numbers, here termed portal matter (PM), also exist. The presence of such types of states and the strong suggestion of a need to embed U(1)DU(1)D​ into a non-abelian gauge structure not too far above the TeV scale based on the RGE running of the U(1)DU(1)D​ gauge coupling is potentially indicative of an enlarged group linking together the visible and dark sectors. The gauge group G=SU(3)c×SU(3)L×U(1)A×U(1)B=3c3L1A1BG=SU(3)c​×SU(3)L​×U(1)A​×U(1)B​=3c​3L​1A​1B​ is perhaps the simplest setup wherein the SM and dark interactions are partially unified in a non-abelian fashion that is not a simple product group of the form G=GSM×GDG=GSM​×GD​ encountered frequently in earlier work. The present paper describes the implications and phenomenology of this type of setup.

Rizzo, Thomas G. [SLAC National Accelerator Labora↗
DOE OSTI2023

Soft particles and infinite-dimensional geometry

Abstract In the sigma model, soft insertions of moduli scalars enact parallel transport ofS-matrix elements about the finite-dimensional moduli space of vacua, and the antisymmetric double-soft theorem calculates the curvature of the vacuum manifold. We explore the analogs of these statements in gauge theory and gravity in asymptotically flat spacetimes, where the relevant moduli spaces are infinite-dimensional. These models have spaces of vacua parameterized by (trivial) flat connections on the celestial sphere, and soft insertions of photons, gluons, and gravitons parallel transportS-matrix elements about these infinite-dimensional manifolds. We argue that the antisymmetric double-soft gluon theorem ind + 2 bulk dimensions computes the curvature of a connection on the infinite-dimensional space Map ( S d , G ) / G , whereGis the global part of the gauge group. The analogous metrics in abelian gauge theory and gravity are flat, as indicated by the vanishing of the antisymmetric double-soft theorems in those models. In other words, Feynman diagram calculations not only know about the vacuum manifold of Yang–Mills theory, they can also be used to compute its curvature. The results have interesting implications for flat space holography.

Astronomy & Astrophysics↗
DOE OSTI2025

Toward UV models of kinetic mixing and portal matter. VII. A light dark photon in the 3 𝑐 ⁢3 𝐿 ⁢1 𝐴 ⁢1 𝐵 model

The kinetic mixing (KM) portal, by which the Standard Model (SM) photon mixes with a light dark photon arising from a new 𝑈⁢(1) 𝐷 gauge group, allows for the possibility of viable scenarios of sub-GeV thermal dark matter with appropriately suppressed couplings to the SM. This KM can only occur if particles having both SM and dark quantum numbers, here termed portal matter, also exist. The presence of such types of states and the strong suggestion of a need to embed 𝑈⁢(1) 𝐷 into a non-Abelian gauge structure not too far above the TeV scale based on the renormalization-group equation running of the 𝑈⁢(1)𝐷 gauge coupling is potentially indicative of an enlarged group linking together the visible and dark sectors. The gauge group 𝐺 = 𝑆⁢𝑈⁢(3) 𝑐 × 𝑆⁢𝑈⁢(3) 𝐿 × 𝑈⁢(1) 𝐴 × 𝑈⁢(1) 𝐵 = 3 𝑐 ⁢3 𝐿 ⁢1 𝐴 ⁢1 𝐵 is perhaps the simplest setup wherein the SM and dark interactions are partially unified in a non-Abelian fashion that is not a simple product group of the form 𝐺 = 𝐺 SM × 𝐺 𝐷 encountered frequently in earlier work. The present paper describes the implications and phenomenology of this type of setup.

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 OSTI2020

Symmetry-enriched quantum spin liquids in (3 + 1)d

We use the intrinsic one-form and two-form global symmetries of (3+1)d bosonic field theories to classify quantum phases enriched by ordinary (0-form) global symmetry. Different symmetry-enriched phases correspond to different ways of coupling the theory to the background gauge field of the ordinary symmetry. The input of the classification is the higher-form symmetries and a permutation action of the 0-form symmetry on the lines and surfaces of the theory. From these data we classify the couplings to the background gauge field by the 0-form symmetry defects constructed from the higher-form symmetry defects. For trivial two-form symmetry the classification coincides with the classification for symmetry fractionalizations in (2 + 1)d. We also provide a systematic method to obtain the symmetry protected topological phases that can be absorbed by the coupling, and we give the relative ’t Hooft anomaly for different couplings. We discuss several examples including the gapless pure U(1) gauge theory and the gapped Abelian finite group gauge theory. As an application, we discover a tension with a conjectured duality in (3 + 1)d for SU(2) gauge theory with two adjoint Weyl fermions.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗
DOE OSTI2020

Gluon field digitization via group space decimation for quantum computers

Efficient digitization is required for quantum simulations of gauge theories. Schemes based on discrete subgroups use fewer qubits at the cost of systematic errors. We systematize this approach by deriving a single plaquette action for approximating general continuous gauge groups through integrating out field fluctuations. This provides insight into the effectiveness of these approximations, and how they could be improved. We accompany the scheme by simulations of pure gauge over the largest discrete subgroup of SU(3) up to the third order.

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS↗