Superstring in the plane-wave background with RR flux as a conformal field theory

TL;DR

This paper formulates the superstring in a plane-wave background with RR flux as an exact conformal field theory, reconciling non-linear couplings with conformal symmetry and confirming the physical spectrum via BRST analysis.

Contribution

It constructs an exact conformal field theory description of the superstring in a plane-wave background with RR flux, despite inherent left-right couplings.

Findings

Two independent sets of Virasoro operators are constructed.

BRST cohomology reproduces the light-cone gauge spectrum.

The theory maintains conformal symmetry with non-linear couplings.

Abstract

We study the type IIB superstring in the plane-wave background with Ramond-Ramond flux and formulate it as an exact conformal field theory in operator formalism. One of the characteristic features of the superstring in a consistent background with RR flux, such as the AdS5xS5 and its plane-wave limit, is that the left- and the right-moving degrees of freedom on the worldsheet are inherently coupled. In the plane-wave case, it is manifested in the well-known fact that the Green-Schwarz formulation of the theory reduces to that of free massive bosons and fermions in the light-cone gauge. This raises the obvious question as to how this feature is reconciled with the underlying conformal symmetry of the string theory. By adopting the semi-light-cone conformal gauge, we will show that, despite the existence of such non-linear left-right couplings, one can construct two independent sets of quantum Virasoro operators in terms of fields obeying the free-field commutation relations. Furthermore, we demonstrate that the BRST cohomology analysis reproduces the physical spectrum obtained in the light-cone gauge.