Michael Faux

Adinkras : A graphical technology for supersymmetric representation theory

We present a symbolic method for organizing the representation theory of one-dimensional superalgebras. This relies on special objects, which we have called adinkra symbols, which supply tangible geometric forms to the still-emerging mathematical basis underlying supersymmetry.

Codes and supersymmetry in one dimension

Adinkras are diagrams that describe many useful supermultiplets in D=1 dimensions. We show that the topology of the Adinkra is uniquely determined by a doubly even code. Conversely, every doubly even code produces a possible topology of an Adinkra. A computation of doubly even codes results in an enumeration of these Adinkra topologies up to N=28, and for minimal supermultiplets, up to N=32.

N = 2 supergravity Lagrangians with vector-tensor multiplets

We discuss the coupling of vector-tensor multiplets to N = 2 supergravity.

The vector-tensor supermultiplet with gauged central charge

The vector-tensor multiplet is coupled off-shell to an N = 2 vector multiplet such that its central charge transformations are realized locally. A gauged central charge is a necessary prerequisite for a coupling to supergravity and the strategy underlying our construction uses the potential for such a coupling as a guiding principle. The results for the action and transformation rules take a nonlinear form and necessarily include a Chern-Simons term. After a duality transformation the action is encoded in a homogeneous holomorphic function consistent with special geometry.

Intersecting orbifold planes and local anomaly cancellation in M-theory

Abstract A systematic program is developed for analyzing and canceling local anomalies on networks of intersecting orbifold planes in the context of M-theory. Through a delicate balance of factors, it is discovered that local anomaly matching on the lower-dimensional intersection of two orbifold planes may require twisted matter on those planes which do not conventionally support an anomaly (such as odd-dimensional planes). In this way, gravitational anomalies can, in principle, tell us about (twisted) gauge groups on subspaces which are not necessarily ten-, six- or two-dimensional. An example is worked out for the case of an S 1 Z 2 × T 4 Z 2 orbifold and possible implications for four-dimensional physics are speculated on.

Dimensional Enhancement via Supersymmetry

We explain how the representation theory associated with supersymmetry in diverse dimensions is encoded within the representation theory of supersymmetry in one time-like dimension. This is enabled by algebraic criteria, derived, exhibited, and utilized in this paper, which indicate which subset of one-dimensional supersymmetric models describes “shadows” of higher-dimensional models. This formalism delineates that minority of one-dimensional supersymmetric models which can “enhance” to accommodate extra dimensions. As a consistency test, we use our formalism to reproduce well-known conclusions about supersymmetric field theories using one-dimensional reasoning exclusively. And we introduce the notion of “phantoms” which usefully accommodate higher-dimensional gauge invariance in the context of shadow multiplets in supersymmetric quantum mechanics.

On the matter of N=2 matter

Abstract 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.

Chern-Simons Couplings and Inequivalent Vector-Tensor Multiplets

The off-shell vector-tensor multiplet is considered in an arbitrary background of N = 2 vector supermultiplets. We establish the existence of two inequivalent versions, characterized by different Chern-Simons couplings. In one version the vector field of the vector-tensor multiplet is contained quadratically in the Chem-Simons term, which implies non-linear terms in the supersymmetry transformations and equations of motion. In the second version, which requires a background of at least two abelian vector supermultiplets, the supersymmetry transformations remain at most linear in the vector-tensor components. This version is of the type known to arise from reduction of tensor supermultiplets in six dimensions. Our work applies to any number of vector-tensor multiplets.

Spin holography via dimensional enhancement

Abstract We explain how all information about ambient component field spin assignments in higher-dimensional off-shell supersymmetry is accessibly coded in one-dimensional restrictions, known as shadows. We also explain how to determine whether the components of a given one-dimensional supermultiplet may assemble into representations of spin ( 1 , D − 1 ) and, if so, how to specifically determine those representations.

Local anomaly cancellation, M-theory orbifolds and phase-transitions

In this paper we consider orbifold compactifications of M-theory on S1/Z2×T4/Z2. We discuss solutions of the local anomaly matching conditions by twisted vector, tensor and hypermultiplets confined on the local orbifold six-planes. In addition we consider phase-transitions among different solutions which are mediated by M-theory fivebranes which touch the local orbifold planes and are converted there to gauge instantons.