The AdS(5)xS(5) Semi-Symmetric Space Sine-Gordon Theory

TL;DR

This paper explores a class of integrable field theories related to superstrings on AdS(5)xS(5), revealing an exotic supersymmetry, constructing soliton solutions, and analyzing their semi-classical quantization and spectrum.

Contribution

It introduces a semi-symmetric space sine-Gordon model for AdS(5)xS(5), uncovers a novel N=(8,8) supersymmetry, and analyzes soliton solutions and their quantization.

Findings

Existence of an exotic N=(8,8) supersymmetry in the theory.

Construction of soliton solutions with internal moduli space.

Quantization of solitons yields a spectrum of massive states in short representations.

Abstract

The generalized symmetric space sine-Gordon theories are a series of 1+1-integrable field theories that are classically equivalent to superstrings on symmetric space spacetimes F/G. They are formulated in terms of a semi-symmetric space as a gauged WZW model with fermions and a potential term to deform it away from the conformal fixed point. We consider in particular the case of PSU(2,2|4)/Sp(2,2)xSp(4) which corresponds to AdS(5)xS(5). We argue that the infinite tower of conserved charges of these theories includes an exotic N=(8,8) supersymmetry that is realized in a mildy non-local way at the Lagrangian level. The supersymmetry is associated to a double central extension of the superalgebra psu(2|2)+psu(2|2) and includes a non-trivial R symmetry algebra corresponding to global gauge transformations, as well as 2-dimensional spacetime translations. We then explicitly construct soliton solutions and show that they carry an internal moduli superspace CP(2|1)xCP(2|1) with both bosonic and Grassmann collective coordinates. We show how to semi-classical quantize the solitons by writing an effective quantum mechanical system on the moduli space which takes the form of a co-adjoint orbit of SU(2|2)xSU(2|2). The spectrum consists of a tower of massive states in the short, or atypical, symmetric representations, just as the giant magnon states of the string world sheet theory, although here the tower is truncated.