Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability

TL;DR

This paper demonstrates that duality transformations in the AdS5 x S5 superstring preserve integrability and superconformal symmetry, revealing a deep connection between dual models and conserved charges in string theory.

Contribution

It shows that duality transformations extend to the full superstring, preserving integrability and superconformal symmetry, and maps conserved charges between local and non-local types.

Findings

Duality maps the superstring action into itself in a different gauge.

The Lax connection remains invariant under duality, indicating preserved integrability.

Dual models interchange local and non-local conserved charges.

Abstract

We discuss 2d duality transformations in the classical AdS5 x S5 superstring and their effect on the integrable structure. T-duality along four directions in Poincare parametrization of AdS5 maps the bosonic part of the superstring action into itself. On bosonic level, this duality may be understood as a symmetry of the first-order (phase space) system of equations for the coset components of the current. The associated Lax connection is invariant modulo the action of an so(2,4)-automorphism. We then show that this symmetry extends to the full superstring, provided one supplements the transformation of the bosonic components of the current with a transformation on the fermionic ones. At the level of the action, this symmetry can be seen by combining the bosonic duality transformation with a similar one applied to part of the fermionic superstring coordinates. As a result, the full superstring action is mapped into itself, albeit in a different kappa-symmetry gauge. One implication is that the dual model has the same superconformal symmetry group as the original one, and this may be seen as a consequence of the integrability of the superstring. The invariance of the Lax connection under the duality implies a map on the full set of conserved charges that should interchange some of the Noether (local) charges with hidden (non-local) ones and vice versa.