From world-sheet supersymmetry to super target spaces

TL;DR

This paper explores the connection between world-sheet supersymmetry and supergroup WZNW models, revealing how superconformal structures relate to supergroup models and their applications in string theory.

Contribution

It demonstrates that B-twisting superconformal sigma models yields supergroup WZNW models and expresses superconformal currents via superalgebra currents, providing new insights into protected sectors and boundary actions.

Findings

Superconformal sigma models relate to supergroup WZNW models through B-twist.

Superconformal currents can be expressed in terms of Lie superalgebra currents.

Application to string theory on AdS_3 x S^3 x T^4 shows practical relevance.

Abstract

We investigate the relation between N=(2,2) superconformal Lie group WZNW models and Lie supergroup WZNW models. The B-twist of an exactly marginal perturbation of the world-sheet superconformal sigma model is the supergroup model. Moreover, the superconformal currents are expressed in terms of Lie superalgebra currents in the twisted theory. As applications, we find protected sectors and boundary actions in the supergroup sigma model. A special example is the relation between string theory on AdS_3 x S^3 x T^4 in the RNS formalism and the U(1,1|2) x U(1|1) x U(1|1) supergroup WZNW model.