Three-dimensional (p,q) AdS superspaces and matter couplings

TL;DR

This paper introduces and analyzes various three-dimensional (p,q) AdS superspaces, exploring their geometry and constructing off-shell supersymmetric sigma-models, revealing conditions for superconformal invariance and specific target space geometries.

Contribution

It defines new (p,q) AdS superspaces in 3D, classifies their geometries, and constructs explicit off-shell sigma-models with detailed target space conditions.

Findings

All (p,q) AdS superspaces with X^{IJKL}=0 are conformally flat.

(3,0) AdS supersymmetry requires superconformal sigma-models with hyperkahler cone target spaces.

(2,1) AdS supersymmetry constrains target spaces to non-compact hyperkahler manifolds with SO(2) symmetry.

Abstract

We introduce N-extended (p,q) AdS superspaces in three space-time dimensions, with p+q=N and p>=q, and analyse their geometry. We show that all (p,q) AdS superspaces with X^{IJKL}=0 are conformally flat. Nonlinear sigma-models with (p,q) AdS supersymmetry exist for p+q<=4 (for N>4 the target space geometries are highly restricted). Here we concentrate on studying off-shell N=3 supersymmetric sigma-models in AdS_3. For each of the cases (3,0) and (2,1), we give three different realisations of the supersymmetric action. We show that (3,0) AdS supersymmetry requires the sigma-model to be superconformal, and hence the corresponding target space is a hyperkahler cone. In the case of (2,1) AdS supersymmetry, the sigma-model target space must be a non-compact hyperkahler manifold endowed with a Killing vector field which generates an SO(2) group of rotations of the two-sphere of complex structures.