Bäcklund transformations, energy shift and the plane wave limit

We discuss basic properties of the Bäcklund transformations for the classical string in AdS space in the context of the null-surface perturbation theory. We explain the relation between the Bäcklund transformations and the energy shift of the dual field theory state. We show that the Bäcklund transformations can be represented as a finite-time evolution generated by a special linear combination of the Pohlmeyer charges. This is a manifestation of the general property of Bäcklund transformations known as spectrality. We also discuss the plane wave limit

Giant Gravitons from Holomorphic Surfaces

We introduce a class of supersymmetric cycles in spacetimes of the form AdS times a sphere or $T^{1,1}$ which can be considered as generalizations of the giant gravitons. Branes wrapped on these cycles preserve $1\over 2$, $1\over 4$ or $1\over 8$ of the supersymmetry. On the CFT side these configurations correspond to superpositions of the large number of BPS states.Comment: LaTeX, 21p

Pure spinors in AdS and Lie algebra cohomology

We show that the BRST cohomology of the massless sector of the Type IIB superstring on AdS5xS5 can be described as the relative cohomology of an infinite-dimensional Lie superalgebra. We explain how the vertex operators of ghost number 1, which correspond to conserved currents, are described in this language. We also give some algebraic description of the ghost number 2 vertices, which appears to be new. We use this algebraic description to clarify the structure of the zero mode sector of the ghost number two states in flat space, and initiate the study of the vertices of the higher ghost number.Comment: 39pp. LaTeX; v2: corrections in Section 4; v3: expanded Section 4.10, added reference; v4: added example of a vertex at the ghost number 3 in Section 5.3, removed Section 4.9, added explanations; v5: corrections in Sections 3.3 and 4.

Sine-Gordon-like action for the Superstring in AdS(5) x S(5)

We propose an action for a sine-Gordon-like theory, which reproduces the classical equations of motion of the Green-Schwarz-Metsaev-Tseytlin superstring on AdS(5) x S(5). The action is relativistically invariant. It is a mass-deformed gauged WZW model for SO(4,1) x SO(5) / SO(4) x SO(4) interacting with fermions.Comment: 19 pages, LaTeX; v2: added discussion of zero modes in Section 3; v3: improved presentatio