Exactly solvable model of superstring in Ramond-Ramond plane wave background

TL;DR

This work provides an exact solution for Type IIB superstrings in the maximally supersymmetric RR plane-wave background by showing the light-cone Green–Schwarz action is quadratic in both bosons and fermions. The authors perform complete canonical quantization, derive the harmonic-oscillator structure of the Hamiltonian, and construct the light-cone realization of the plane-wave supersymmetry algebra, including the subtle zero-mode sector and its vacuum choices. They explicitly compute the Type IIB supergravity fluctuation spectrum in this background, demonstrating a discrete zero-mode spectrum that matches specific SO(4)×SO'(4) representations, and present a light-cone superfield formulation that unifies bosonic and fermionic fluctuations. The results illuminate the plane-wave limit of AdS/CFT, provide a tractable arena for comparing string and supergravity spectra, and set the stage for further calculations such as vertex operators and D-brane configurations in this background.

Abstract

We describe in detail the solution of type IIB superstring theory in the maximally supersymmetric plane-wave background with constant null Ramond-Ramond 5-form field strength. The corresponding light-cone Green-Schwarz action found in hep-th/0112044 is quadratic in both bosonic and fermionic coordinates. We find the spectrum of the light-cone Hamiltonian and the string representation of the supersymmetry algebra. The superstring Hamiltonian has a ``harmonic-oscillator'' form in both the string-oscillator and the zero-mode parts and thus has discrete spectrum in all 8 transverse directions. We analyze the structure of the zero-mode sector of the theory, establishing the precise correspondence between the lowest-lying ``massless'' string states and the type IIB supergravity fluctuation modes in the plane-wave background. The zero-mode spectrum has certain similarity to the supergravity spectrum in AdS_5 x S^5 of which the plane-wave background is a special limit. We also compare the plane-wave string spectrum with expected form of the light-cone gauge spectrum of superstring in AdS_5 x S^5.