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

• Published in: arXiv.org 2003-08
• Main Author: Nedel, Daniel L
• Format: Article
• Language: English
• Subjects: Compensators; Consistency; Dilatons; Equations of motion; Invariance; Mathematical models; Supergravity; Supersymmetry; Tensors
• ISSN: 2331-8422
• DOI: 10.48550/arxiv.0306166

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.