Aleph-Null Extended Supergravity and Chern-Simons Theories

Abstract

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.

17 pages, LATEX file, all macros included

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• Strong Coupling and the Cosmological Constant
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Cited by in corpus (9)

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• Chiral Symmetry and the Cosmological Constant
• Non-Linear Realization of ${\aleph }_0$-Extended Supersymmetry
• Topologican Gauging of N=16 Supergravity in Three-Dimensions
• The Background Field Method for N = 2, d3 Super Chern-Simons-Matter Theories
• Supersymmetric E_{8(+8)} / SO(16) Sigma-Model Coupled to N=1 Supergravity in Three-Dimensions
• Alephnull-Extended Supersymmetric Chern-Simons Theory for Arbitrary Gauge Groups
• Off-shell construction of superconformal Chern-Simons theories in three dimensions
• Aleph_null Hypergravity in Three-Dimensions