Dual Superconformal Symmetry from AdS5 x S5 Superstring Integrability

TL;DR

The paper demonstrates that a bosonic T-duality along four AdS5 directions acts as a symmetry of the AdS5×S5 superstring's phase-space and Lax structure, with the duality extended to fermions via a compensating transformation. When combined, these dualities map the full superstring action to itself in a different κ-gauge, preserving the full PSU(2,2|4) symmetry and integrable hierarchy. Consequently, the dual model shares the same superconformal symmetry, and the conserved charges reorganize into a mix of local Noether and nonlocal hidden charges, revealing a deep link between integrability and dual superconformal invariance. This duality framework offers a route to understanding the bulk/boundary symmetry correspondence in AdS/CFT and the role of dual conformal structures in the spectrum of the theory.

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.