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S. James Gates Jr

Publications and source records attributed to S. James Gates Jr.

At least 19 recordsLinked to original sources
arXiv2026

10D Supergravity Numerical Data Sets for L & R Matrices

After reviewing the development of 10D, superspace theories, and their relations to superstring and heterotic string theories, explicit calculations are undertaken in the on-shell $\cal N$ = 1 linearized supergravity, the associated super-current is derived, and non-closure terms are explicitly given. The $L_{\rm I}$ and $R_{\rm I}$ adjacency matrices are then computed in complete numerical form as data sets. This is the preliminary step required to perform a scan to embed the on-shell matrices into off-shell ones.

hep-th↗
arXiv2026

Quantum Information Approach to Bosonization of Supersymmetric Yang-Mills Fields

We consider bosonization of supersymmetry in the context of Wess-Zumino quantum mechanics. Our motivation for this investigation is the flexibility the bosonic fock space affords as any classical probability distribution can be realized on it making it a versatile framework to work with for quantum processes. We proceed by constructing a minimal bosonization of a system with one bosonic and two fermionic degrees of freedom. We iterate this process to construct a tower of SUSY systems that is akin to unfolded Adinkras. We then identify an osp(2|2) symmetry of the system constructed. To build an irreducible representation of the system we induce representations across the sectors, a first to our knowledge, as the previous work have focused on induction only within the bosonic sector. First, we start with a fermionic representation using Clifford algebras and then induce a representation to gl(2|2) and restrict it to osp(2|2). In the second method, we induce a representation from that of the bosonic sector. In both cases, our representations are in terms of qubit operators that provide a way to solve SUSY problems using quantum information based approaches. Depending upon the direction of induction the representations are suitable for implementation on a hybrid qubit and fermionic or bosonic quantum computers.

quant-ph↗
arXiv2024

A combinatorial introduction to Adinkras

We survey the combinatorics of the Adinkra, a graphical device for solving differential equations in supersymmetry. These graphs represent an exceptional class of 1-factorizations with further augmentations. As a new feature, we characterize Adinkras using Latin rectangles.

math.HO↗
arXiv2023

Towards A Direct Detection of the Spin of Dark Matter

We investigate the contribution of higher spin particles in the signal of direct detection experiments searching for dark matter. We consider a bosonic or fermionic higher spin dark matter (HSDM) candidate which interacts with the Standard Model via a dark U(1) mediator. For a particular subclass of interactions, spin-polarized targets may be used for spin determination: The angular dependence of scatterings can distinguish integer (spin-$s$) vs. half-integer (spin-$s + 1/2$), while the recoil energy dependence of the signal determines $s$. We consider also the signal of a supersymmetric higher spin dark sector, which suggests a characteristic signal (''SUSY Rilles'') for directional direct detection.

hep-ph↗
arXiv2021

The 300 "Correlators" Suggests 4D, $\cal N$ = 1 SUSY Is a Solution to a Set of Sudoku Puzzles

A conjecture is made that the weight space for 4D, $\cal N$-extended supersymmetrical representations is embedded within the permutahedra associated with permutation groups ${\mathbb{S}}{}_{d}$. Adinkras and Coxeter Groups associated with minimal representations of 4D, $\cal N$ = 1 supersymmetry provide evidence supporting this conjecture. It is shown the appearance of the mathematics of 4D, $\cal N$ = 1 minimal off-shell supersymmetry representations is equivalent to solving a four color problem on the truncated octahedron. This observation suggest an entirely new way to approach the off-shell SUSY auxiliary field problem based on IT algorithms probing the properties of ${\mathbb{S}}{}_{d}$.

hep-th↗
arXiv2020

A Letter Highlighting Matrix Mapping in Minimal 4D, ${\mathbf {\cal N}}$ = 1 On-Shell Supermultiplet Representations

On the basis of comparing eigenvalues of an operator ${\hat {\mathbf{\cal C}}}{}^{({\cal R})}$, that proved useful in distinguishing how off-shell 4D, $\cal N$ = 1 supermultiplets become off-shell 4D, $\cal N$ = 2 supermultiplets, the double tensor supermultiplet is shown to be radically different for other known multiplets. This suggests difficulties, if not impossibilities, to embed it into an off-shell structure.

hep-th↗
arXiv2016

A Proposal On Culling & Filtering A Coxeter Group For 4D, N = 1 Spacetime SUSY Representations

We review the mathematical tools required to cull and filter representations of the Coxeter Group $BC_4$ into providing bases for the construction of minimal off-shell representations of the 4D, $ {\cal N}$ = 1 spacetime supersymmetry algebra. Of necessity this includes a description of the mathematical mechanism by which four dimensional Lorentz symmetry appears as an emergent symmetry in the context of one dimensional adinkras with four colors described by the Coxeter Group $BC_4$.

hep-th↗
arXiv2012

Adinkra Isomorphisms and `Seeing' Shapes with Eigenvalues

We create an algorithm to determine whether any two graphical representations (adinkras) of equations possessing the property of supersymmetry in one or two dimensions are isomorphic in shape. The algorithm is based on the determinant of `permutation matrices' that are defined in this work and derivable for any adinkra.

hep-th↗
arXiv2012

SUSY Equation Topology, Zonohedra, and the Search for Alternate Off-Shell Adinkras

Results are given from a search to form adinkra-like equations based on topologies that are not hypercubes. An alternate class of zonohedra topologies are used to construct adinkra-like graphs. In particular, the rhombic dodecahedron and rhombic icosahedron are studied in detail. Using these topological skeletons, equations similar to those of a supersymmetric system are found. But these fail to have the interpretation of an off-shell supersymmetric system of equations.

math.RT↗
arXiv2012

Adinkra (In)Equivalence From Coxeter Group Representations: A Case Study

Using a Mathematica code, we present a straightforward numerical analysis of the 384-dimensional solution space of signed permutation 4x4 matrices, which in sets of four provide representations of the GR(4,4) algebra, closely related to the N=1 (simple) supersymmetry algebra in 4-dimensional spacetime. Following after ideas discussed in previous papers about automorphisms and classification of adinkras and corresponding supermultiplets, we make a new and alternative proposal to use equivalence classes of the (unsigned) permutation group S4 to define distinct representations of higher dimensional spin bundles within the context of adinkras. For this purpose, the definition of a dual operator akin to the well-known Hodge star is found to partition the space of these GR(4,4) representations into three suggestive classes.

hep-th↗
arXiv2012

Adinkras and SUSY Holography

We discuss the mechanism by which adinkras holographically store the required information for the Spin(1,3) Clifford Algebra fiber bundle in the cases of three 4D, N=1 representations: the chiral, vector and tensor supermultiplets.

hep-th↗
arXiv2012

4D, N = 1 Supersymmetry Genomics (II)

We continue the development of a theory of off-shell supersymmetric representations analogous to that of compact Lie algebras such as SU(3). For off-shell 4D, N = 1 systems, quark-like representations have been identified [1] in terms of cis-Adinkras and trans-Adinkras and it has been conjectured that arbitrary representations are composites of $n_c$-cis and $n_t$-trans representations. Analyzing the real scalar and complex linear superfield multiplets, these "chemical enantiomer" numbers are found to be $n_c$ = $n_t$ = 1 and $n_c$ = 1, $n_t$ = 2, respectively.

hep-th↗
arXiv2011

A Unified Spinorial Superfield Treatment of the Higher Superspin Superfield Formalism

We discuss the higher superspin superfield formalism of Kuzenko et al from the basis of a unified treatment of an unconstrained spinorial superfield prepotential, its action and a restricted set of gauge transformations. We recover previous results as distinct limits of this unified treatment and give the first derivations of the complete set of Bianchi identities associated with these equations.

hep-th↗
arXiv2008

Short Distance Operator Product Expansion of the 1D, N = 4 Extended GR Super Virasoro Algebra by Use of Coadjoint Representations

Using the previous construction of the geometrical representation (GR) of the centerless 1D, N = 4 extended Super Virasoro algebra, we construct the corresponding Short Distance Operation Product Expansions for the deformed version of the algebra. This algebra differs from the regular algebra by the addition of terms containing the Levi-Civita tensor. How this addition changes the super-commutation relations and affects the Short Distance Operation Product Expansions (OPEs) of the associated fields is investigated. The Method of Coadjoint Orbits, which removes the need first to find Lagrangians invariant under the action of the symmetries, is used to calculate the expansions. Finally, an alternative method involving Clifford algebras is investigated for comparison.

hep-th↗
arXiv2005

Can the string scale be related to the cosmic baryon asymmetry?

In a previous work, a mechanism was presented by which baryon asymmetry can be generated during inflation from elliptically polarized gravitons. Nonetheless, the mechanism only generated a realistic baryon asymmetry under special circumstances which requires an enhancement of the lepton number from an unspecified GUT. In this note we provide a stringy embedding of this mechanism through the Green-Schwarz mechanism, demonstrating that if the model-independent axion is the source of the gravitational waves responsible for the lepton asymmetry, one can observationally constrain the string scale and coupling.

hep-th↗
arXiv2003

Short Distance Expansion from the Dual Representation of Infinite Dimensional Lie Algebras

We compute the short distance expansion of fields or operators that live in the coadjoint representation of an infinite dimensional Lie algebra by using only properties of the adjoint representation and its dual. We explicitly compute the short distance expansion for the duals of the Virasoro algebra, affine Lie Algebras and the geometrically realized N-extended supersymmetric GR Virasoro algebra.

hep-th↗
arXiv2003

When Superspace Is Not Enough

We give an expanded discussion of the proposal that spacetime supersymmetry representations may be viewed as having their origins in 1D theories that involve a special class of real Clifford algebras. These 1D theories reproduce the supersymmetric structures of spacetime supersymmetric theories after the latter are reduced on a 0-brane.

hep-th↗