arXiv subjects

S. James Gates, Jr.

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

At least 37 records · Page 2Linked to original sources

arXiv2019

Integer superspin supercurrents of matter supermultiplets

In recent papers we demonstrated that consistent and non-trivial \emph{linear} transformations of matter supermultiplets generate half-integer superspin supercurrents and the cubic interactions between matter and half-integer superspin supermultiplets. In this work we show that consistent and non-trivial \emph{antilinear} transformations of matter superfields lead to the construction of integer superspin supercurrents and the cubic interactions between mater and integer superspin supermultiplets. Applying Noether's method to these transformations, we find new integer superspin supercurrents for the case of a free massless chiral superfield. Furthermore, we use them to find new integer superspin supercurrent multiplets for a massive chiral superfield and a chiral superfield with a linear superpotential. Also various selection rules for such interactions are found.

hep-th↗

arXiv2019

On Linearized Nordstr\" om Supergravity in Eleven and Ten Dimensional Superspaces (2)

We present aspects of the component description of linearized Nordstr\" om Supergravity in eleven and ten dimensions. The presentation includes low order component fields in the supermultiplet, the supersymmetry variations of the scalar graviton and gravitino trace, their supercovariantized field strengths, and the supersymmetry commutator algebra of these theories.

hep-th↗

arXiv2019

Generating all 36,864 Four-Color Adinkras via Signed Permutations and Organizing into $\ell$- and $\tilde{\ell}$-Equivalence Classes

Recently, all 1,358,954,496 values of the gadget between the 36,864 adinkras with four colors, four bosons, and four fermions have been computed. In this paper, we further analyze these results in terms of $BC_3$, the signed permutation group of three elements, and $BC_4$, the signed permutation group of four elements. It is shown how all 36,864 adinkras can be generated via $BC_4$ boson $\times$ $BC_3$ color transformations of two quaternion adinkras that satisfy the quaternion algebra. An adinkra inner product has been used for some time, known as the \emph{gadget}, which is used to distinguish adinkras. We~show how 96 equivalence classes of adinkras that are based on the gadget emerge in terms of $BC_3$ and $BC_4$. We also comment on the importance of the gadget as it relates to separating out dynamics in terms of Kähler-like potentials. Thus, on the basis of the complete analysis of the supersymmetrical representations achieved in the preparatory first four sections, the final comprehensive achievement of this work is the construction of the universal $BC_4$ non-linear $σ$-model.

hep-th↗

arXiv2019

Exploring the Abelian 4D, $\mathcal{N}$ = 4 Vector-Tensor Supermultiplet and Its Off-Shell Central Charge Structure

An abelian 4D, $\mathcal{N}$ = 4 vector supermultiplet allows for a duality transformation to be applied to one of its spin-0 states. The resulting theory can be described as an abelian 4D, $\mathcal{N}$ = 4 vector-tensor supermultiplet. It is seen to decompose into a direct sum of an off-shell 4D, $\mathcal{N}$ = 2 vector supermultiplet and an off-shell 4D, $\mathcal{N}$ = 2 tensor supermultiplet. The commutator algebra of the other two supersymmetries are still found to be on-shell. However, the central charge structure in the resulting 4D, $\mathcal{N}$ = 4 vector-tensor supermultiplet is considerably simpler that that of the parent abelian 4D, $\mathcal{N}$ = 4 vector supermultiplet. This appears to be due to the replacement of the usual SO(4) symmetry associated with the abelian 4D, $\mathcal{N}$ = 4 vector supermultiplet being replaced by a GL(2,$\mathbb{R}$)$\otimes$GL(2,$\mathbb{R}$) symmetry in the 4D, $\mathcal{N}$ = 4 vector-tensor supermultiplet. The $Mathematica$ code detailing the calculations is available open-source at the HEPTHools Data Repository on GitHub.

hep-th↗

arXiv2017

On the Four Dimensional Holoraumy of the 4D, $\cal N$ = 1 Complex Linear Supermultiplet

We present arguments to support the existence of weight spaces for supersymmetric field theories and identify the calculations of information about supermultiplets to define such spaces via the concept of "holoraumy." For the first time this is extended to the complex linear supermultiplet by a calculation of the commutator of supercovariant derivatives on all of its component fields.

hep-th↗

arXiv2015

Think Different: Applying the Old Macintosh Mantra to the Computability of the SUSY Auxiliary Field Problem

Starting with valise supermultiplets obtained from 0-branes plus field redefinitions, valise adinkra networks, and the "Garden Algebra," we discuss an architecture for algorithms that (starting from on-shell theories and, through a well-defined computation procedure), search for off-shell completions. We show in one dimension how to directly attack the notorious "off-shell auxiliary field" problem of supersymmetry with algorithms in the adinkra network-world formulation.

hep-th↗

arXiv2014

Adinkra `Color' Confinement In Exemplary Off-Shell Constructions Of 4D, ${\cal N}$ = 2 Supersymmetry Representations

Evidence is presented in some examples that an adinkra quantum number, $χ_{\rm o}$ (arXiv:\ 0902.3830 [hep-th]), seems to play a role with regard to off-shell 4D, $\cal N$ = 2 SUSY similar to the role of color in QCD. The vanishing of this adinkra quantum number appears to be a condition required for when two off-shell 4D, $\cal N$ = 1 supermultiplets form an off-shell 4D, $\cal N$ = 2 supermultiplet. We also explicitly comment on a deformation of the Lie bracket and anti-commutator operators that has been extensively and implicitly used in our work on "Garden Algebras" adinkras, and codes.

hep-th↗

arXiv2013

Reduction Redux of Adinkras

We show performing general "0-brane reduction" along an arbitrary fixed direction in spacetime and applied to the starting point of minimal, off-shell 4D, $\cal N$ $=$ 1 irreducible supermultiplets, yields adinkras whose adjacency matrices are among some of the special cases proposed by Kuznetsova, Rojas, and Toppan. However, these more general reductions also can lead to `Garden Algebra' structures beyond those described in their work. It is also shown that for light-like directions, reduction to the 0-brane breaks the equality in the number of fermions and bosons for dynamical theories. This implies that light-like reductions should be done instead to the space of 1-branes or equivalently to the worldsheet.

hep-th↗

arXiv2013

On 4D, N = 1 Massless Gauge Superfields of Higher Superspin: Integer Case

We present an alternative method of exploring the component structure of an integer super-helicity Y=s (for any integers) irreducible representation of the Super-Poincare group. We use it to derive the component action and the SUSY transformation laws. The effectiveness of this approach is based on the equations of motion and their properties, like Bianchi identities. These equations are generated by the superspace action when it is expressed in terms of prepotentials. For that reason we reproduce the superspace action for integer superspin, using unconstrained superfields. The appropriate, to use, superfields are dictated by the representation theory of the group and the requirement that there is a smooth limit between the massive and massless case.

hep-th↗

arXiv2013

A Dynamical Theory for Massive Supergravity

We present a new massive theory of superspin Y=3/2 which has non-minimal supergravity as it's massless limit. The new result will illuminate the underlying structure of auxiliary fields required for the description of arbitrary massive half-integer superspin systems.

hep-th↗

arXiv2013

4D, N=1 Supergravity Genomics

The off-shell representation theory of 4D, $\mathcal{N}=1$ supermultiplets can be categorized in terms of distinct irreducible graphical representations called adinkras as part of a larger effort we call supersymmetry `genomics.' Recent evidence has emerged pointing to the existence of three such fundamental adinkras associated with distinct equivalence classes of a Coxeter group. A partial description of these adinkras is given in terms of two types, termed cis-and trans-adinkras (the latter being a degenerate doublet) in analogy to cis/trans isomers in chemistry. Through a new and simple procedure that uses adinkras, we find the irreducible off-shell adinkra representations of 4D, $\mathcal{N}=1$ supergravity, in the old-minimal, non-minimal, and conformal formulations. This procedure uncovers what appears to be a selection rule useful to reverse engineer adinkras to higher dimensions. We categorize the supergravity representations in terms of the number of cis-($n_c$) and trans-($n_t$) adinkras in the representation and synthesize our new results with our previous supersymmetry genomics results into a group theoretic framework.

hep-th↗

arXiv2011

A Codicil To Massless Gauge Superfields of Higher Half-Odd Integer Superspins

We study theories of 4D, N=1 supersymmetric massless, arbitrary higher half odd-integer superspins. A new series of such theories is found to exist for arbitrary superspin Y (Y=s+1/2 for any integer s). The lowest member (s=1) of the series is the original off-shell formulation of 4D, N=1 supergravity first presented by Breitenlohner in 1977.

hep-th↗

arXiv2011

A Codicil To Massless Gauge Superfields of Higher Integer Superspins

We study theories of 4D, N=1 supersymmetric massless, arbitrary integer superspins. A new state-of-the art is being established by the discovery of a new series of such theories for arbitrary superspin Y (Y=s for any integer s) The lowest member of the series is surprisingly found to be a previously established formulation of the spin (3/2, 1) supermultiplet.

hep-th↗

arXiv2007

D=2 N=(2,2) Semi Chiral Vector Multiplet

We describe a new 1+1 dimensional N=(2,2) vector multiplet that naturally couples to semi chiral superfields in the sense that the gauged supercovariant derivative algebra is only consistent with imposing covariantly semi chiral superfield constraints. It has the advantages that its prepotentials shift by semi chiral superfields under gauge transformations. We also see that the multiplet relates the chiral vector multiplet with the twisted chiral vector multiplet by reducing to either multiplet under appropriate limits without being reducible in terms of the chiral and twisted chiral vector multiplet. This is explained from the superspace geometrical point of view as the result of possessing a symmetry under the discrete supercoordinate transformation that is responsible for mirror copies of supermultiplets. We then describe how to gauge a non linear sigma model with semi chiral superfields using the prepotentials of the new multiplet.

hep-th↗

arXiv2006

New massive supergravity multiplets

We present new off-shell formulations for the massive superspin-3/2 multiplet. In the massless limit, they reduce respectively to the old minimal (n=-1/3) and non-minimal ($n\neq -1/3, 0$) linearized formulations for 4D N=1 supergravity. Duality transformations, which relate the models constructed, are derived.

hep-th↗

arXiv2006

Off-shell supersymmetry and filtered Clifford supermodules

An off-shell representation of supersymmetry is a representation of the super Poincare algebra on a dynamically unconstrained space of fields. We describe such representations formally, in terms of the fields and their spacetime derivatives, and we interpret the physical concept of engineering dimension as an integral grading. We prove that formal graded off-shell representations of one-dimensional N-extended supersymmetry, i.e., the super Poincare algebra p^{1|N}, correspond to filtered Clifford supermodules over Cl(N). We also prove that formal graded off-shell representations of two-dimensional (p,q)-supersymmetry, i.e., the super Poincare algebra p^{1,1|p,q}, correspond to bifiltered Clifford supermodules over Cl(p+q). Our primary tools are the formal deformations of filtered superalgebras and supermodules, which give a one-to-one correspondence between filtered spaces and graded spaces with even degree-shifting injections. This generalizes the machinery developed by Gerstenhaber to prove that every filtered algebra is a deformation of its associated graded algebra. Our treatment extends Gerstenhaber's discussion to the case of filtrations which are compatible with a supersymmetric structure, as well as to filtered modules in addition to filtered algebras. We also describe the analogous constructions for bifiltrations and bigradings.

math-ph↗

arXiv2005

Massive 4D, N = 1 Superspin 1 & 3/2 Multiplets and Dualities

Lagrangians for several new off-shell 4D, N = 1 supersymmetric descriptions of massive superspin-1 and superspin-3/2 multiplets are described. Taken together with the models previously constructed, there are now four off-shell formulations for the massive gravitino multiplet (superspin-1) and six off-shell formulations for the massive graviton multiplet (superspin-3/2). Duality transformations are derived which relate some of these dynamical systems.

hep-th↗

arXiv2004

Field Strengths of Linearized 5D, N = 1 Superfield Supergravity On a 3-Brane

Recently a description of linearized 5D supergravity in 4D, N =1 superspace was presented. By analyzing the on-shell component Lagrangian, this description was proven to be Lorentz invariant in five dimensions. This paper describes a geometric formulation of the 5D supergravity in 4D, N =1 superspace. Using this new formalism, the on-shell structure of the previous description is verified from purely superspace methods. This geometric description provides a connection to dimensionally reduced manifestly supersymmetric 5D supergravity.

hep-th↗