Superconformal sigma models in three dimensions

Abstract

We construct superconformal gauged sigma models with extended rigid supersymmetry in three dimensions. Those with N > 4 have necessarily flat targets, but the models with N ≤ 4 admit non-flat targets, which are cones with appropriate Sasakian base manifolds. Superconformal symmetry also requires that the three dimensional spacetimes admit conformal Killing spinors which we examine in detail. We present explicit results for the gauged superconformal theories for N = 1, 2. In particular, we gauge a suitable subgroup of the isometry group of the cone in a superconformal way. We finally show how these sigma models can be obtained from Poincaré supergravity. This connection is shown to necessarily involve a subset of the auxiliary fields of supergravity for N ≥ 2.

Supersymmetric gauge theories in three dimensions

“…This leads to more possibilities for constructing superconformal gaugings with possibly non-trivial worldvolumes and/or target spaces. These cases are presently under study [24].…”

Massive N $$ \mathcal{N} $$ = 2 supergravity in three dimensions

“…The conformal N = 2 supergravity, and the two-derivative invariants were considered in [8][9][10][11]. Off-shell matter-coupled suprgravity theories were investigated in the superspace framework in [12][13][14][15].…”

“…The off-shell N = (1, 1) Poincaré supergravity and the supersymmetric completion of the cosmological term are already given in the literature, and they are also referred to as Type I minimal supergravity or three dimensional old minimal supergravity [8][9][10]12]. Here we shall derive them from the superconformal tensor calculus point of view, which will also serve to establish our notation and conventions.…”

Higher spin supermultiplets in three dimensions: (2,0) AdS supersymmetry

“…Unlike four dimensions, where pure N = 1 AdS supergravity is unique on-shell, the feature specific to three dimensions is the existence of two distinct N = 2 AdS supergravity theories [11], which are known as the (1,1) and (2,0) AdS supergravity theories, originally constructed as Chern-Simons theories. Two off-shell formulations for (1,1) AdS supergravity have been developed, the minimal [12,13,14,15,16,17,18] and the nonminimal [17,18] theories, and one for (2,0) AdS supergravity [19,16,17,18]. Since there are three off-shell N = 2 AdS supergravity theories, one might expect the existence of three series of massless higher-spin gauge supermultiplets.…”