Superstring action in AdS_5 x S^5: kappa symmetry light cone gauge

TL;DR

The paper provides a concrete construction of the Green-Schwarz superstring action in $AdS_5 \times S^5$ in a fermionic light-cone $\kappa$-symmetry gauge, yielding a theory with quadratic and quartic fermionic terms that remains well-behaved in the flat-space and superparticle limits. By formulating the action through the $psu(2,2|4)$ superalgebra in a light-cone basis and expressing it with Cartan forms, the authors derive explicit light-cone gauge fixed expressions and a 2-d spinor reformulation that clarifies the SU(4) structure and background couplings. The work also systematically addresses bosonic gauge fixing and the passage to a 2-d spinor description, establishing a framework to explore quantization and AdS/CFT correspondence in a controllable LC setting. Overall, this furnishes a practical LC gauge framework for the AdS$_5\times S^5$ superstring, potentially aiding spectrum analyses and connections to the boundary ${\cal N}=4$ SYM theory.

Abstract

As part of program to quantize superstrings in AdS_5 x S^5 background in light cone approach we find the explicit form of the corresponding Green-Schwarz action in fermionic light-cone kappa-symmetry gauge. The resulting action is quadratic and quartic in fermions. In the flat space limit it reduces to the standard light-cone Green-Schwarz action, and also has the correct superparticle limit. We discuss fixing the bosonic light-cone gauge and a reformulation of the action in terms of 2-d Dirac spinors.