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S. J. Gates Jr

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

11 recordsLinked to original sources
arXiv2012

A Computer Algorithm For Engineering Off-Shell Multiplets With Four Supercharges On The World Sheet

We present an adinkra-based computer algorithm implemented in a Mathematica code and use it in a limited demonstration of how to engineer off-shell, arbitrary N-extended world-sheet supermultiplets. Using one of the outputs from this algorithm, we present evidence for the unexpected discovery of a previously unknown 8 - 8 representation of N = 2 world sheet supersymmetry. As well, we uncover a menagerie of (p, q) = (3, 1) world sheet supermultiplets.

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arXiv2012

The Real Anatomy of Complex Linear Superfields

Recent work on classicication of off-shell representations of N-extended worldline supersymmetry without central charges has uncovered an unexpectedly vast number--trillions of even just (chromo)topology types--of so called adinkraic supermultiplets. Herein, we show by explicit analysis that a long-known but rarely used representation, the complex linear supermultiplet, is not adinkraic, cannot be decomposed locally, but may be reduced by means of a Wess-Zumino type gauge. This then indicates that the already unexpectedly vast number of adinkraic off-shell supersymmetry representations is but the proverbial tip of the iceberg.

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arXiv2008

Relating Doubly-Even Error-Correcting Codes, Graphs, and Irreducible Representations of N-Extended Supersymmetry

Previous work has shown that the classification of indecomposable off-shell representations of N-supersymmetry, depicted as Adinkras, may be factored into specifying the topologies available to Adinkras, and then the height-assignments for each topological type. The latter problem being solved by a recursive mechanism that generates all height-assignments within a topology, it remains to classify the former. Herein we show that this problem is equivalent to classifying certain (1) graphs and (2) error-correcting codes.

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arXiv2006

6D Supersymmetry, Projective Superspace and 4D, N=1 Superfields

In this note, we establish the formulation of 6D, N=1 hypermultiplets in terms of 4D chiral-nonminimal (CNM) scalar multiplets. The coupling of these to 6D, N=1 Yang-Mills multiplets is described. A 6D, N=1 projective superspace formulation is given in which the above multiplets naturally emerge. The covariant superspace quantization of these multiplets is studied in details.

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arXiv2004

Dynamical Equations from a First-Order Perturbative Superspace Formulation of 10D N=1 String-Corrected Supergravity (I)

Utilizing a first-order perturbative superspace approach, we derive the bosonic equations of motion for the 10D, N = 1 supergravity fields. We give the Lagrangian corresponding to these equations derived from superspace geometry. Moreover, the equivalence of this Lagrangian to the first-order perturbative component level Lagrangian of anomaly-free supergravity is proven. Our treatment covers both the two-form and six-form formulations.

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arXiv2002

Is Stringy-Supersymmetry Quintessentially Challenged?

We discuss the problem of introducing background spacetimes of the de Sitter type (quintessential backgrounds) in the context of fundamental theories involving supersymmetry. The role of a model presented in 1984, showing that these backgrounds can occur as spontaneously broken phases of locally supersymmetric 4D, N-extended theories, is highlighted. The present twin challenges of the presumed presence of supersymmetry in particle physics and the emergence of experimental evidence for a positive cosmological constant from type-II supernovae data are noted for the continued investigation of superstring/M-theory. Finally we note how the 1984-model may have a role to play in future investigations.

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arXiv1996

On Aspects and Implications of the New Covariant 4D, N = 1 Green-Schwarz Sigma-model Action

Utilizing (2,0) superfields, we write a supersymmetry-squared action and partially relate it to the new formulation of the Green-Schwarz action given by Berkovits and Siegel. Recent results derived from this new formulation are discussed within the context of some prior proposals in the literature. Among these, we note that 4D, N = 1 beta-FFC superspace geometry with a composite connection for R-symmetry has now been confirmed as the only presently known limit of 4D, N = 1 heterotic string theory that is derivable in a completely rigorous manner.

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arXiv1996

Why Auxiliary Fields Matter: The Strange Case of the 4D, N = 1 Supersymmetric QCD Effective Action (II)

Within a four dimensional N = 1 superspace, we present a new ansatz for the Skyrme term and for the gauged WZNW term embedded into a superaction. We use the new chiral-nonminimal (CNM) formulation for the effective low-energy action of 4D, N = 1 supersymmetric QCD constructed by assigning right-handed components of Dirac fields to chiral multiplets and left-handed components of Dirac fields to nonminimal multiplets. It is noted that such a construction likely allows for a new type of parity violation in low-energy 4D, N = 1 supersymmetric QCD.

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arXiv1994

Extended Supersymmetry and Super-BF Gauge Theories

The absence of fermion kinetic terms in supersymmetric-BF gauge theories is established. We do this by means of explicit off-shell (superspace) constructions. As part of our study we give the superspace constraints for D=3, N=4 super Yang-Mills along with the D=3, N=4 superconformal algebra. The puzzle we are interested in solving is the fact that the topological cousins, known as super-BF gauge theories, of certain supersymmetric-BF theories have kinetic terms for the twisted fermions. We show that the map which takes the latter to the former includes a Hodge decomposition of the twisted fermions. In conjunction with this result, we argue that it is natural to modify the naive path integral measure of supersymmetric-BF theories to include the Ray-Singer analytic torsion.

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