Weyl covariance, and proposals for superconformal prepotentials in 10D superspaces

Proposals are made to describe the Weyl scaling transformation laws of supercovariant derivatives ∇A, the torsion supertensors TABC, and curvature supertensors RABcd in 10D superspaces. Starting from the proposal that an unconstrained supergravity prepotential for the 11D, $$ \mathcal{N} $$ N = 1 theory is described by a scalar superfield, considerations for supergravity prepotentials in the 10D theories are enumerated. We derive infinitesimal 10D superspace Weyl transformation laws and discover ten possible 10D, $$ \mathcal{N} $$ N = 1 superfield supergravity prepotentials. The first identification of all off-shell ten dimensional supergeometrical Weyl field strength tensors, constructed from respective torsions, is presented.

Solving the 2D SUSY Gross-Neveu-Yukawa model with conformal truncation

We use Lightcone Conformal Truncation to analyze the RG flow of the two-dimensional supersymmetric Gross-Neveu-Yukawa theory, i.e. the theory of a real scalar superfield with a ℤ2-symmetric cubic superpotential, aka the 2d Wess-Zumino model. The theory depends on a single dimensionless coupling $$ \overline{g} $$ g ¯ , and is expected to have a critical point at a tuned value $$ {\overline{g}}_{\ast } $$ g ¯ ∗ where it flows in the IR to the Tricritical Ising Model (TIM); the theory spontaneously breaks the ℤ2 symmetry on one side of this phase transition, and breaks SUSY on the other side. We calculate the spectrum of energies as a function of $$ \overline{g} $$ g ¯ and see the gap close as the critical point is approached, and numerically read off the critical exponent ν in TIM. Beyond the critical point, the gap remains nearly zero, in agreement with the expectation of a massless Goldstino. We also study spectral functions of local operators on both sides of the phase transition and compare to analytic predictions where possible. In particular, we use the Zamolodchikov C-function to map the entire phase diagram of the theory. Crucial to this analysis is the fact that our truncation is able to preserve supersymmetry sufficiently to avoid any additional fine tuning.

Adinkra foundation of component decomposition and the scan for superconformal multiplets in 11D, $$ \mathcal{N} $$ = 1 superspace

For the first time in the physics literature, the Lorentz representations of all 2,147,483,648 bosonic degrees of freedom and 2,147,483,648 fermionic degrees of freedom in an unconstrained eleven dimensional scalar superfield are presented. Comparisons of the conceptual bases for this advance in terms of component field, superfield, and adinkra arguments, respectively, are made. These highlight the computational efficiency of the adinkra-based approach over the others. It is noted at level sixteen in the 11D, $$ \mathcal{N} $$ N = 1 scalar superfield, the {65} representation of SO(1,10), the conformal graviton, is present. Thus, adinkra-based arguments suggest the surprising possibility that the 11D, $$ \mathcal{N} $$ N = 1 scalar superfield alone might describe a Poincaré supergravity prepotential or semi-prepotential in analogy to one of the off-shell versions of 4D, $$ \mathcal{N} $$ N = 1 superfield supergravity. We find the 11D, $$ \mathcal{N} $$ N = 1 scalar superfield contains 1,494 bosonic fields, 1,186 fermionic fields, and a maximum number of 29,334 links connecting them via orbits of the supercharges.

Playing with the enveloping algebra of supersymmetry

In this paper, we show how to obtain from a scalar superfield its first component via a similarity transformation. We prove that in [Formula: see text] the generators of this similarity transformation live in the enveloping algebra of supersymmetry while for [Formula: see text] they belong to the basic algebra.

PREPOTENTIALS FOR (2, 2) SUPERGRAVITY

We present a complete solution to the constraints for two-dimensional N = 2 supergravity in N = 2 superspace. We obtain explicit expressions for the covariant derivatives in terms of the vector superfield Hm and, for the two versions of minimal (2,2) supergravity, a chiral or twisted chiral scalar superfield ϕ.

SUPERFIELD FORMULATION OF CHERN-SIMONS SUPERSYMMETRY

We discuss an extra supersymmetry present in the covariantly quantized Chern-Simons action within the superfield formalism. By introducing scalar superfields we show how the component transformations are naturally reproduced from the superfield transformation. When the superspace is extended to include an additional odd coordinate for the BRST symmetry, the entire theory is described by a single odd scalar superfield. The implications of this supersymmetry for the renormalized theory are also discussed.