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

TL;DR

This paper provides an exact solution for type IIB superstring theory in a maximally supersymmetric plane-wave background, revealing a discrete spectrum and detailed correspondence with supergravity modes, advancing understanding of string dynamics in curved backgrounds.

Contribution

It presents an exactly solvable model of superstring theory in a plane-wave background with explicit spectrum and supersymmetry algebra, extending previous formulations.

Findings

Spectrum has a harmonic-oscillator form with discrete energies.

Zero-mode states correspond to supergravity fluctuation modes.

Comparison with AdS_5 x S^5 spectrum shows similarities.

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.