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.Comment: 39 pages, references adde
