Type IIB Green-Schwarz superstring in plane wave Ramond-Ramond background

TL;DR

This work constructs a covariant κ-symmetric Type IIB superstring action on a plane-wave Ramond-Ramond background using a coset G/H sigma-model, then fixes both fermionic and bosonic light-cone gauges to obtain a quadratic, explicitly solvable 2d theory. The author derives the explicit Lagrangian and Hamiltonian in the light-cone gauge, analyzes the equations of motion, and provides a complete set of Noether charges that realize the plane-wave supersymmetry algebra. The results demonstrate that the plane-wave RR background yields an exact, quantizable string model with a discrete, bounded-below spectrum and offer a controlled setting to compare with AdS5×S5 RR backgrounds and to inform NSR formulations. The paper thus provides a concrete, tractable framework for studying Type IIB strings in RR backgrounds and lays groundwork for deeper holographic connections.

Abstract

We construct the covariant $κ$-symmetric superstring action for type $IIB$ superstring on plane wave space supported by Ramond-Ramond background. The action is defined as a 2d sigma-model on the coset superspace. We fix the fermionic and bosonic light-cone gauges in the covariant Green-Schwarz superstring action and find the light-cone string Lagrangian and the Hamiltonian. The resulting light-cone gauge action is quadratic in both the bosonic and fermionic superstring 2d fields, and therefore, this model can be explicitly quantized. We also obtain a realization of the generators of the basic superalgebra in terms of the superstring 2d fields in the light-cone gauge.