Pohlmeyer reduction for superstrings in AdS space

Abstract

The Pohlmeyer reduced equations for strings moving only in the AdS subspace of AdS5 × S5 have been used recently in the study of classical Euclidean minimal surfaces for Wilson loops and some semiclassical three-point correlation functions. We find an action that leads to these reduced superstring equations. For example, for a bosonic string in AdSn such an action contains a Liouville scalar part plus a K/K gauged WZW model for the group K = SO(n − 2) coupled to another term depending on two additional fields transforming as vectors under K. Solving for the latter fields gives a non-Abelian Toda model coupled to the Liouville theory. For n = 5 we generalize this bosonic action to include the S5 contribution and fermionic terms. The corresponding reduced model for the AdS2 × S2 truncation of the full AdS5 × S5 superstring turns out to be equivalent to super Liouville theory. Our construction is based on taking a limit of the previously found reduced theory actions for bosonic strings in AdSn × S1 and superstrings in AdS5 × S5. This new action may be useful as a starting point for possible quantum generalizations or deformations of the classical Pohlmeyer-reduced theory. We give examples of simple extrema of this reduced superstring action which represent strings moving in the AdS5 part of the space. Expanding near these backgrounds we compute the corresponding fluctuation spectra and show that they match the spectra found in the original superstring theory.