On reduced models for superstrings on AdS_n x S^n

TL;DR

The work shows how the Green-Schwarz superstring on $AdS_n\times S^n$ can be recast through Pohlmeyer reduction as a gauged WZW model with an integrable potential and fermions, enabling a tractable description of reduced dynamics. In the $AdS_3\times S^3$ case, the bosonic sector becomes a direct sum of the complex sine-Gordon and its hyperbolic counterpart, while the fermionic sector is explicitly incorporated; the authors also analyze an axial gauging and discuss potential $N=2$ 2d supersymmetry in a truncation. The paper further develops the general framework for reductions on group manifolds, relates the results to AdS$_2$ and AdS$_5$ reductions, and comments on vacuum structure, perturbative expansions, and the relation between reduced and original string solutions. These insights provide a pathway toward a more accessible, integrable formulation of string dynamics in AdS backgrounds and clarify the role of gauge choices and hidden symmetries in the reduced theories.

Abstract

We review the Pohlmeyer reduction procedure of the superstring sigma model on AdS_n x S^n leading to a gauged WZW model with an integrable potential coupled to 2d fermions. In particular, we consider the case of the Green-Schwarz superstring on AdS_3 x S^3 supported by RR flux. The bosonic part of the reduced model is given by the sum of the complex sine-Gordon Lagrangian and its sinh-Gordon counterpart. We determine the corresponding fermionic part and discuss possible existence of hidden 2d supersymmetry in the reduced action. We also elaborate on some general aspects of the Pohlmeyer reduction applied to the AdS_5 x S^5 superstring.