Low Energy Action of "Covariant" Superstring Field Theory in the NS-NS pp-Wave Background

TL;DR

This paper constructs a covariant low energy superstring field theory in the NS-NS pp-wave background, demonstrating its invariance and exact correspondence with supergravity perturbations, advancing understanding of string dynamics in curved backgrounds.

Contribution

It provides the first covariant formulation of the low energy superstring field action in the NS-NS pp-wave background without gauge fixing, and proves its equivalence to supergravity perturbations.

Findings

The constructed action is world-sheet BRST invariant.

There is an exact correspondence with supergravity second-order perturbation.

Gauge transformations are consistent between string field theory and supergravity.

Abstract

Exact construction of superstring field theory in some background fields is very important. We construct the low energy NS-NS sector of superstring field action in the pp-wave background with the flux of NS-NS antisymmetric tensor field (NS-NS pp-wave) without gauge fixing up to the second-order where the action is world-sheet BRST invariant. Here we use the word "covariant" in a invariant theory for a symmetric transformation of the pp-wave background which is not the Lorentz transformation in the flat background. Moreover we prove the exact correspondence between this low energy action and the second-order perturbation of supergravity action in the same background. We also prove the correspondence of the gauge transformation in both the actions. This construction is based on the BRST first quantization of superstrings in the pp-wave background in our previous paper.