Aleph-Null Extended Supergravity and Chern-Simons Theories

TL;DR

This paper introduces a new class of three-dimensional supergravity theories with unlimited supersymmetries, coupling them to Chern-Simons and BF theories, and explores their dimensional reductions to lower dimensions.

Contribution

It generalizes extended supergravity to arbitrarily many supersymmetries without central charges and couples these theories to Chern-Simons and BF theories, overcoming previous limitations.

Findings

Successfully coupled \u2205null supergravity to Chern-Simons and BF theories.

Demonstrated dimensional reduction from 4D to 3D and 2D theories.

Provided a new  supergravity Liouville model.

Abstract

We give generalizations of extended Poincar\'e 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.