Dual superconformal symmetry from AdS5×S5 superstring integrability

We discuss 2d duality transformations in the classical AdS₅×S⁵ superstring and their effect on the integrable structure. T-duality along four directions in the Poincaré parametrization of AdS₅ maps the bosonic part of the superstring action into itself. On the 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 κ-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 (nonlocal) ones and vice versa.