Sugawara form for AdS superstring

TL;DR

This paper demonstrates that the stress-energy tensor of the AdS5xS5 superstring can be expressed in a supersymmetric Sugawara form using right-invariant currents, incorporating Wess-Zumino terms and ensuring kappa invariance.

Contribution

It introduces a supersymmetric generalized Sugawara form for the AdS superstring's stress-energy tensor, accounting for Wess-Zumino terms and demonstrating kappa invariance.

Findings

Stress-energy tensor expressed as supertrace of squared right-invariant current

Inclusion of Wess-Zumino term via supersymmetric gauge connection

Infinite conserved currents from integrability, related to Virasoro and kappa constraints

Abstract

We show that the stress-energy tensor for a superstring in the AdS5xS5 background is written in a supersymmetric generalized "Sugawara" form. It is the "supertrace" of the square of the right-invariant current which is the Noether current satisfying the flatness condition. The Wess-Zumino term is taken into account through the supersymmetric gauge connection in the right-invariant currents, therefore the obtained stress-energy tensor is kappa invariant. The integrability of the AdS superstring provides an infinite number of the conserved "local" currents which are supertraces of the n-th power of the right-invariant current. For even n the "local" current reduces to terms proportional to the Virasoro constraint and the kappa symmetry constraint, while for odd n it reduces to a term proportional to the kappa symmetry constraint .