arXiv subjects
Publications and source records attributed to S. J. Gates, Jr..
We provide an introduction to the concepts of holoraumy tensors, Lorentz covariant four-dimensional "Gadgets", and Gadget angles within the context of 4D N = 2 supermultiplets. This is followed by the calculation of the holoraumy tensors, Gadgets, and Gadget angles for minimal off-shell supermultiplets. Four tetrahedrons in four 3D subspaces of the Holoraumy lattice space are found.
A Gadget, more precisely a scalar Gadget, is defined as a mathematical calculation acting over a domain of one or more adinkra graphs and whose range is a real number. A 2010 work on the subject of automorphisms of adinkra graphs, implied the existence of multiple numbers of Gadgets depending on the number of colors under consideration. For four colors, this number is two. In this work, we verify the existence of a second such Gadget and calculate (both analytically and via explicit computer-enabled algorithms) its 1,358,954,496 matrix elements over 36,864 minimal valise adinkras related to the Coxeter Group BC4.
Starting from three minimal off-shell 4D, $\cal N$ = 1 supermultiplets, using constructions solely defined within the confines of the four dimensional field theory we show the existence of a "gadget" - a member of a class of metrics on the representation space of the supermultiplets - whose values directly and completely correspond to the values of a metric defined on the 1d, $N$ = 4 adinkra networks adjacency matrices corresponding to the projections of the four dimensional supermultiplets.
We present evidence of the existence of a 1D, N = 16 SUSY hologram that can be used to understand representation theory aspects of a 4D, N = 4 supersymmetrical vector multiplet. In this context, the long-standing off-shell "SUSY problem" for the 4D, N = 4 Maxwell supermultiplet is precisely formulated as a problem in linear algebra.
A minimal representation of the N = 8 extended worldline supersymmetry, known as the `ultra-multiplet', is closely related to a family of supermultiplets with the same, E(8) chromotopology. We catalogue their effective symmetries and find a Spin(4) x Z(2) subgroup common to them all, which explains the particular basis used in the original construction. We specify a constrained superfield representation of the supermultiplets in the ultra-multiplet family, and show that such a superfield representation in fact exists for all adinkraic supermultiplets. We also exhibit the correspondences between these supermultiplets, their Adinkras and the E(8) root lattice bases. Finally, we construct quadratic Lagrangians that provide the standard kinetic terms and afford a mixing of an even number of such supermultiplets controlled by a coupling to an external 2-form of fluxes.
The recent classification scheme of so-called adinkraic off-shell supermultiplets of N-extended worldline supersymmetry without central charges finds a combinatorial explosion. Completing our earlier efforts, we now complete the constructive proof that all of these trillions or more of supermultiplets have a superfield representation. While different as superfields and supermultiplets, these are still super-differentially related to a much more modest number of minimal supermultiplets, which we construct herein.
We explain how the redefinitions of supermultiplet component fields, comprising what we call "frame shifts", can be used in conjuction with the graphical technology of multiplet Adkinras to render manifest the reducibility of off-shell representations of supersymmetry. This technology speaks to possibility of organizing multiplet constraints in a way which complements and extends the possibilities afforded by superspace methods.
We present further progress toward a complete classification scheme for describing supermultiplets of N-extended worldline supersymmetry, which relies on graph-theoretic topological invariants. In particular, we demonstrate a relationship between Adinkra diagrams and quotients of N-dimensional cubes, where the quotient groups are subgroups of $(Z_2)^N$. We explain how these quotient groups correspond precisely to doubly even binary linear error-correcting codes, so that the classification of such codes provides a means for describing equivalence classes of Adinkras and therefore supermultiplets. Using results from coding theory we exhibit the enumeration of these equivalence classes for all cases up to 26 supercharges, as well as the maximal codes, corresponding to minimal supermultiplets, for up to 32 supercharges.
We construct a model of an electrically charged magnetic dipole with arbitrary N-extended world-line supersymmetry, which exhibits a supersymmetric Zeeman effect. By including supersymmetric constraint terms, the ambient space of the dipole may be tailored into an algebraic variety, and the supersymmetry broken for almost all parameter values. The so exhibited obstruction to supersymmetry breaking refines the standard one, based on the Witten index alone.
We introduce a variety of four-dimensional N = 2 matter multiplets which have not previously appeared explicitly in the literature. Using these, we develop a class of supersymmetric actions supplying a context for a systematic exploration of N = 2 matter theories, some of which include Hypermultiplet sectors in novel ways. We construct an N = 2 supersymmetric field theory in which the propagating fields are realized off-shell exclusively as Lorentz scalars and Weyl spinors and which involves a sector with precisely the R-charge assignments characteristic of Hypermultiplets.
We present a counter-example to the recent claim that supermultiplets of N-extended supersymmetry with no central charge and in 1-dimension are specified unambiguously by providing the numbers of component fields in all available engineering dimensions within the supermultiplet.
Using 4D, N=1 superfield techniques, a discussion of the 6D sigma-model possessing simple supersymmetry is given. Two such approaches are described. Foremost it is shown that the simplest and most transparent description arises by use of a doublet of chiral scalar superfields for each 6D hypermultiplet. A second description that is most directly related to projective superspace is also presented. The latter necessarily implies the use of one chiral superfield and one nonminimal scalar superfield for each 6D hypermultiplet. A separate study of models of this class, outside the context of projective superspace, is also undertaken.
We demonstrate a method for describing one-dimensional N-extended supermultiplets and building supersymmetric actions in terms of unconstrained prepotential superfields, explicitly working with the Scalar supermultiplet. The method uses intuitive manipulations of Adinkras and GR(d,N) algebras, a variant of Clifford algebras. In the process we clarify the relationship between Adinkras, GR(d,N) algebras, and superspace.
In this paper we discuss off-shell representations of N-extended supersymmetry in one dimension, ie, N-extended supersymmetric quantum mechanics, and following earlier work on the subject codify them in terms of certain graphs, called Adinkras. This framework provides a method of generating all Adinkras with the same topology, and so also all the corresponding irreducible supersymmetric multiplets. We develop some graph theoretic techniques to understand these diagrams in terms of a relatively small amount of information, namely, at what heights various vertices of the graph should be "hung". We then show how Adinkras that are the graphs of N-dimensional cubes can be obtained as the Adinkra for superfields satisfying constraints that involve superderivatives. This dramatically widens the range of supermultiplets that can be described using the superspace formalism and organizes them. Other topologies for Adinkras are possible, and we show that it is reasonable that these are also the result of constraining superfields using superderivatives. The family of Adinkras with an N-cubical topology, and so also the sequence of corresponding irreducible supersymmetric multiplets, are arranged in a cyclical sequence called the main sequence. We produce the N=1 and N=2 main sequences in detail, and indicate some aspects of the situation for higher N.
We use the method of Banerjee, Banerjee and Mitra and minimal homotopy paths to compute the consistent gauge anomaly for several superspace models of SSYM coupled to matter. We review the derivation of the anomaly for N=1 in four dimensions and then discuss the anomaly for two-dimensional models with (2,0) supersymmetry.
We discuss the possibility of the existence of a long-lived top squark ($τ\ll 10^{10} years$) and its motivation. If the stop is indeed metastable, it forms hadrons. We study properties of the low-energy stop-containing hadrons and their signatures in collider experiments.
We give generalizations of extended Poincaré supergravity with {\it arbitrarily many} supersymmetries in the absence of central charges in three-dimensions by gauging its intrinsic global $~SO(N)$~ symmetry. We call these \alephnull (Aleph-Null) supergravity theories. We further couple a non-Abelian supersymmetric Chern-Simons theory and an Abelian topological BF theory to \alephnull supergravity. Our result overcomes the previous difficulty for supersymmetrization of Chern-Simons theories beyond $~N=4$. This feature is peculiar to the Chern-Simons and BF theories including supergravity in three-dimensions. We also show that dimensional reduction schemes for four-dimensional theories such as $~N=1$~ self-dual supersymmetric Yang-Mills theory or $~N=1$~ supergravity theory that can generate \alephnull globally and locally supersymmetric theories in three-dimensions. As an interesting application, we present \alephnull supergravity Liouville theory in two-dimensions after appropriate dimensional reduction from three-dimensions.
We study two-dimensional N=2 supersymmetric actions describing general models of scalar and vector multiplets coupled to supergravity.