Supersymmetric Field Theories on AdS_p x S^q

TL;DR

This paper classifies supersymmetry algebras on AdS_p x S^q spaces, exploring their structure and specific cases like 4D theories with N=1 and N=2 supersymmetry on AdS_3 x S^1, highlighting the rich algebraic possibilities.

Contribution

It provides a comprehensive classification of supersymmetry algebras on AdS_p x S^q spaces and analyzes specific supersymmetric field theories in these backgrounds.

Findings

Classification of superconformal algebras on AdS_p x S^q.

Multiple superconformal algebras can arise for the same field theory in AdS_3.

Detailed analysis of 4D N=1 and N=2 theories on AdS_3 x S^1.

Abstract

In this paper we study supersymmetric field theories on an AdS_p x S^q space-time that preserves their full supersymmetry. This is an interesting example of supersymmetry on a non-compact curved space. The supersymmetry algebra on such a space is a (p-1)-dimensional superconformal algebra, and we classify all possible algebras that can arise for p >= 3. In some AdS_3 cases more than one superconformal algebra can arise from the same field theory. We discuss in detail the special case of four dimensional field theories with N=1 and N=2 supersymmetry on AdS_3 x S^1.