In this seminar I will talk about AdS(p) x M(10-p) string models which
occur in various AdS(p) / CFT(p-1)'s. While much is known about the
canonical AdS(5) x S(5) string and its close cousin the AdS(4) x CP(3)
string, less is known about the less symmetric AdS(3) x S(3) x M(4) and
AdS(2) x S(2) x T(6) strings which also appear in AdS / CFT dualities.
As it turns out, both models seem to allow for exact solutions using
tools from integrability such as spin chains and Bethe equations. In
contrast to earlier backgrounds however, a coset construction is not
admissible since fermionic degrees of freedom corresponding to broken
supersymmetries are part of the physical spectrum. Thus one has to
resort to the GS string which nevertheless allow for a rather straight
forward construction of the action. We derive the Lagrangians in a
BMN-like expansion up to quartic order (but only quadratic in
Fermions). We verify that the tree level Bethe equations (up to some
minor ambiguities) successfully reproduces the string energies of some
simple closed subsectors of the theory. We then compute the one loop
corrections to two point functions built out of the bosonic coordinates.
For the AdS(3) string these come with three- and four-vertex
interactions and different masses. This results in a final answer which
seems regularization dependent (very much like the AdS(4) x CP(3)
string). Thus the same ambiguities present in AdS(4) / CFT(3) apply also
here. I will end the talk with some musing about which regulator is
physically motivated.
