Penrose limits and Green-Schwarz strings

TL;DR

This paper analyzes the Green-Schwarz string action in plane-wave backgrounds derived from supergravity solutions, proving its quadratic fermionic form and providing a complete geometric formulation.

Contribution

It establishes the quadratic nature of the light-cone Green-Schwarz action in general plane-wave backgrounds and presents a comprehensive geometric form of the quadratic bosonic action.

Findings

Proves the light-cone action is quadratic in fermions for general backgrounds.

Provides a complete geometric quadratic bosonic action in Einstein and string frames.

Reduces to known actions under specific background conditions.

Abstract

We discuss the Green-Schwarz action for type IIB strings in general plane-wave backgrounds obtained as Penrose limits from any IIB supergravity solutions with vanishing background fermions. Using the normal-coordinate expansion in superspace, we prove that the light-cone action is necessarily quadratic in the fermionic coordinates. This proof is valid for more general pp-wave backgrounds under certain conditions. We also write down the complete quadratic action for general bosonic on-shell backgrounds in a form in which its geometrical meaning is manifest both in the Einstein and string frames. When the dilaton and 1-form field strength are vanishing, and the other field strengths are constant, our string-frame action reduces, up to conventions, to the one which has been written down using the supercovariant derivative.