Consistency of Superspace Low Energy Equations of Motion of 4D Type II Superstring with Type II Sigma Model at Tree-Level

TL;DR

This paper demonstrates the consistency between four-dimensional Type II supergravity equations of motion and the sigma model at tree-level by deriving torsion constraints and analyzing superconformal invariance in superspace.

Contribution

It establishes the superspace torsion constraints and confirms the consistency of Type II supergravity equations with the sigma model at tree-level in a 4D N=2 framework.

Findings

Derived torsion constraints for 4D Type II supergravity.

Showed sigma model's superconformal invariance at tree-level.

Confirmed equations of motion are consistent with the sigma model.

Abstract

We derive the torsion constraints and show the consistency of equations of motion of four-dimensional Type II supergravity in superspace, with Type II sigma model. This is achieved by coupling the four-dimensional compactified Type II Berkovits' superstring to an N=2 curved background and requiring that the sigma-model has superconformal invariance at tree-level. We compute this in a manifestly 4D N=2 supersymmetric way. The constraints break the target conformal and SU(2) invariances and the dilaton will be a conformal, $SU(2)\times U(1)$ compensator. For Type II superstring in four dimensions, worldsheet supersymmetry requires two different compensators. One type is described by chiral and anti-chiral superfields. This compensator can be identified with a vector multiplet. The other Type II compensator is described by twist-chiral and twist-anti-chiral superfields and can be identified with a tensor hypermultiplet. Also, the superconformal invariance at tree-level selects a particular gauge, where the matter is fixed, but not the compensators. After imposing the reality conditions, we show that the Type II sigma model at tree-level is consistent with the equations of motion for Type II supergravity in the string gauge.