The GS String Action on AdS(3)xS(3) with Ramond-Ramond Charge

TL;DR

This work constructs the classical Green–Schwarz string action for Type IIB strings on $AdS_3\times S^3$ with Ramond–Ramond charge by exploiting the $SU(1,1|2)^2$ supercoset structure. It derives the Maurer–Cartan framework, builds a Wess–Zumino term from first principles, and presents a closed-form supergeometry that enables a background-adapted Killing spinor gauge to simplify the action. The resulting form has a drastically reduced fermionic sector, yielding a quadratic-fermion action with explicit $y$-dependent bosonic couplings, facilitating analysis in this RR background albeit without a straightforward quantization procedure. The work provides a concrete, tractable model for RR AdS backgrounds and suggests pathways to connect with NS results and to extract spectra via spacetime symmetries.

Abstract

We derive the classical kappa-symmetric Type IIB string action on AdS(3) x S(3) by employing the SU(1,1|2)^2 algebra. We then gauge fix kappa-symmetry in the background adapted Killing spinor gauge and present the action in a very simple form.