Pohlmeyer reduction for superstrings in AdS space

Abstract

The Pohlmeyer reduced equations for strings moving only in the AdS subspace of AdS5 × 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 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 S 5 contribution and fermionic terms. The corresponding reduced model for the AdS2 × S 2 truncation of the full AdS5 × 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 AdSn × S 1 and superstrings in AdS5 × 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 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.

Wilson loops and minimal area surfaces in hyperbolic space

“…This is the main idea of the Pohlmeyer reduction [59] which we rederive here as it applies to our particular problem. Similar considerations in the context of string theory are well-known, for example see [32][33][34][35][36][37][38][39][40][41][43][44][45][46][47][48][49][50][51][52][53][54][55][56][57] and [60].…”

On string theory on with mixed 3-form flux: Tree-level S-matrix

“…It is of interest to consider the case when the string moves just on AdS 3 [30,55] that corresponds to the limit µ → 0. To take the µ → 0 limit of the Lagrangian (D.20) we should first generalize it by introducing the auxiliary field a ±…”

Wilson loops and Riemann theta functions II

“…In that work the minimal area surfaces were constructed analytically in terms of Riemann theta functions associated to hyperelliptic Riemman surfaces closely following previous work by M. Babich and A. Bobenko [15,16]. It also follows related work where Wilson loops were studied or theta functions were used in similar problems, for example in [17][18][19][20][21][22][23][24][25][26][27][28][29][34][35][36][37][38]. 1 Much of that work was motivated by the relation to scattering amplitudes [28,29] which we do not pursue here.…”