ℵ0-extended supergravity and Chern-Simons theories

Abstract

We give generalizations of extended Poincaré supergravity with arbitrarily many supersymmetries in the absence of central charges in threedimensions by gauging its intrinsic global SO(N) symmetry. We call these ℵ 0 (Aleph-Null) supergravity theories. We further couple a nonAbelian supersymmetric Chern-Simons theory and an Abelian topological BF theory to ℵ 0 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 ℵ 0 globally and locally supersymmetric theories in three-dimensions. As an interesting application, we present ℵ 0 supergravity Liouville theory in two-dimensions after appropriate dimensional reduction from threedimensions.

Low-energy effective actions in three-dimensional extended SYM theories

“…Alternatively, the action (A.1) can be viewed as a BF-type theory coupled to matter chiral superfields. The importance of three-dimensional supersymmetric BF-type theories was pointed out in [34], where the authors studied the coupling of such models to supergravity as well as some aspects of their duality and mirror symmetry. More recently, in [19] it was shown that (A.1) corresponds to the classical action of the Abelian Gaiotto-Witten model [10] which is, in general, a Chern-Simons-matter theory with N = 4 supersymmetry.…”

ℵ0-extended supersymmetric Chern-Simons theory for arbitrary gauge groups

“…The structure of the lagrangian (2.1) is very similar to that in section 2 in [6], but there are also differences. The most important one is that the gauge group G in the present case is completely arbitrary, and the gravitino is in the adjoint representation of G. There is no restriction on the gauge group G.…”

“…Some typical examples were given in [4] with the gauge groups OSp(p|2; IR) ⊗ OSp(q|2; IR), or with N = 8M and N = 8M − 2 supersymmetries in [5], or SO(N) symmetries in [6]. Another example is conformal supergravity CS theory with ∀ N -extended supersymmetries with local SO(N) gauge symmetries [8] [5].…”

Topological gauging ofN=16supergravity in three dimensions

“…Eighth, compared with a model presented in [15], the similarity is that the SO(N) gauge field A µ IJ is minimally coupled to the gravitino, while its field strength is vanishing by the BF -term. The difference is that the present system is more non-trivial, because of the σ -model physical fields on E 8(+8) /SO(16) in addition to other non-propagating fields.…”

“…On the other hand, there has been an independent development related to supersymmetric Chern-Simons theories in 3D [14], in which it has been shown that certain ChernSimons theories in 3D can exist for arbitrary number of supersymmetries up to infinity [15].…”