Pohlmeyer reduction of AdS_5 x S^5 superstring sigma model

TL;DR

The paper develops a Pohlmeyer-type reduction of the AdS5×S5 superstring to a 2d Lorentz-invariant framework described by a gauged WZW model with an integrable potential, supplemented by fermions. By carefully fixing conformal and κ-symmetries and performing a reduction gauge, the authors connect the original FG coset equations to a G/H gauged WZW theory, yielding a local Lagrangian for the physical degrees of freedom. They demonstrate that the reduced theory possesses a massive 8+8 spectrum and exhibits a structure suggestive of 2d supersymmetry, with a concrete AdS2×S2 example realizing N=2 supersymmetric sine-Gordon as a special case. The framework unifies several known reductions (SG/CSG for spheres) with a general AdS5×S5 setting, offering a tractable, UV-finite starting point for studying quantum aspects of the AdS5×S5 superstring and its S-matrix under a current-based, Lorentz-covariant formulation.

Abstract

Motivated by a desire to find a useful 2d Lorentz-invariant reformulation of the AdS_5 x S^5 superstring world-sheet theory in terms of physical degrees of freedom we construct the Pohlmeyer-reduced version of the corresponding sigma model. The Pohlmeyer reduction procedure involves several steps. Starting with a coset space string sigma model in the conformal gauge and writing the classical equations in terms of currents one can fix the residual conformal diffeomorphism symmetry and kappa-symmetry and introduce a new set of variables (related locally to currents but non-locally to the original string coordinate fields) so that the Virasoro constraints are automatically satisfied. The resulting gauge-fixed equations can be obtained from a Lagrangian of a non-abelian Toda type: a gauged WZW model with an integrable potential coupled also to a set of 2d fermionic fields. A gauge-fixed form of the Pohlmeyer-reduced theory can be found by integrating out the 2d gauge field of the gauged WZW model. Its small-fluctuation spectrum contains 8 bosonic and 8 fermionic degrees of freedom with equal masses. We conjecture that the reduced model has world-sheet supersymmetry and is ultraviolet-finite. We show that in the special case of the AdS_2 x S^2 superstring model the reduced theory is indeed supersymmetric: it is equivalent to the N=2 supersymmetric extension of the sine-Gordon model.