The AdS(5)xS(5) Semi-Symmetric Space Sine-Gordon Theory
  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. 
Timothy J. Hollowood and J. Luis Miramontes
hep-th