Pohlmeyer reduction of AdS_5 x S^5 superstring sigma model

TL;DR

This paper develops a Pohlmeyer reduction of the AdS_5 x S^5 superstring sigma model, resulting in an integrable, gauge-fixed 2D theory with potential supersymmetry and finite ultraviolet behavior.

Contribution

It introduces a novel Pohlmeyer reduction procedure for the AdS_5 x S^5 superstring, leading to a gauge-fixed, integrable 2D model with potential supersymmetry and finite UV properties.

Findings

Reduced model contains 8 bosonic and 8 fermionic degrees of freedom with equal masses.

In the AdS_2 x S^2 case, the reduced theory is equivalent to an N=2 supersymmetric sine-Gordon model.

The reduced theory is conjectured to be ultraviolet-finite and supersymmetric.

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.