Abstract
Previous studies of the type IIB superstring in an AdS_5×S^5 background are based on a description of the superspace geometry as the quotient space PSU(2,2|4)/SO(4,1)×SO(5). This paper develops an alternative approach in which the Grassmann coordinates provide a nonlinear realization of PSU(2,2|4) based on the quotient space PSU(2,2|4)/SU(2,2)×SU(4), and the bosonic coordinates are described as a submanifold of SU(2,2)×SU(4). This formulation keeps all bosonic symmetries manifest, and it provides the complete dependence on the Grassmann coordinates in terms of simple analytic expressions. It is used to construct the superstring world-sheet action in a form in which the PSU(2,2|4) symmetry is manifest and kappa symmetry can be established. This formulation might have some advantages compared to previous ones, but this remains to be demonstrated.
Highlights
The isometry supergroup of the AdS5 × S5 solution of type IIB superstring theory is PSU(2, 2|4)
Previous studies of the type IIB superstring in an AdS5 × S5 background are based on a description of the superspace geometry as the quotient space PSU(2, 2|4)/SO(4, 1) × SO(5)
This paper develops an alternative approach in which the Grassmann coordinates provide a nonlinear realization of PSU(2, 2|4) based on the quotient space PSU(2, 2|4)/SU(2, 2) × SU(4), and the bosonic coordinates are described as a submanifold of SU(2, 2) × SU(4)
Summary
Let us briefly review the bosonic structure of. In the large N limit, taken at fixed λ, the CFT is described by the planar approximation, and the string theory is described by the classical approximation, i.e., leading order in the world-sheet genus expansion. The bosonic connections Ω0 and Ω 0 are simultaneously conserved and flat when the equations of motion are taken into account These conditions allow one to construct a oneparameter family of flat connections, whose existence is the key to classical integrability of the world-sheet theory [16]. In the remainder of this manuscript we will add Grassmann coordinates and construct the complete superstring action with PSU(2, 2|4) symmetry Since this will be a “critical” string theory (without conformal anomaly), its integrability is expected to be valid for the quantum theory, i.e., taking full account of the dependence on λ, but only at leading order in the genus expansion
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