Pohlmeyer reduction for superstrings in AdS space

TL;DR

This paper derives an action principle for Pohlmeyer reduced superstring equations in AdS space, linking classical solutions to quantum models and matching fluctuation spectra with original superstring theory.

Contribution

It introduces a new action for the Pohlmeyer reduced superstring equations in AdS space, including fermionic terms and connections to super Liouville theory.

Findings

Derived an action for reduced superstring equations in AdS space.

Connected the reduced model to super Liouville theory for AdS2 x S2.

Matched fluctuation spectra with original superstring theory.

Abstract

The Pohlmeyer reduced equations for strings moving only in the AdS subspace of AdS_5 x S^5 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 AdS_n 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 S^5 contribution and fermionic terms. The corresponding reduced model for the AdS_2 x S^2 truncation of the full AdS_5 x S^5 superstring turns out to be equivalent to N=2 super Liouville theory. Our construction is based on taking a limit of the previously found reduced theory actions for bosonic strings in AdS_n x S^1 and superstrings in AdS_5 x S^5. 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 AdS_5 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.