The type II superstring to order theta^4

TL;DR

This paper derives the Green-Schwarz superstring action in type IIA/IIB backgrounds up to fourth order in fermionic coordinates, providing a detailed expansion useful for understanding superstring dynamics.

Contribution

It presents a systematic derivation of the superstring action up to order theta^4 by solving superspace Bianchi identities, extending previous lower-order results.

Findings

Action terminates at quartic order in theta for many backgrounds.

Explicit expressions for supervielbeins up to theta^4 are obtained.

Kappa symmetry can be fixed to simplify the action.

Abstract

The Green-Schwarz superstring action in a general type IIA or IIB supergravity background is derived up to fourth order in the Grassmann-odd coordinates theta. This is done by solving the superspace Bianchi identities order by order in theta, to quadratic order for all superfields and to quartic order for the supervielbeins. For a large class of backgrounds it is possible to fix the kappa symmetry in such a way that the action actually terminates at the quartic order in theta.