O(d,d;R) Deformations of Complex Structures and Extended Worldsheet Supersymmetry

TL;DR

This paper investigates how O(d,d;R) and O(d,d+16;R) deformations affect complex structures and extended worldsheet supersymmetry in superstring and heterotic string vacua, revealing conditions for preserving superconformal symmetry.

Contribution

It explicitly describes the transformations of complex structures under duality deformations and discusses their impact on extended supersymmetry in string theory backgrounds.

Findings

Deformations preserve extended worldsheet supersymmetry under certain conditions.

Explicit formulas for complex structure transformations are provided.

Generic deformations do not maintain known (2,2) superfield formulations.

Abstract

It is shown that the O(d,d;R) deformations of the superstring vacua and the O(d,d+16;R) deformations of the heterotic string vacua preserve extended worldsheet supersymmetry and, hence, generate superconformal deformations. The transformations of the complex structures are given explicitly and the action of the discrete duality subgroup is discussed. The results are valid when the complex structures are independent of the d coordinates which appear in the transformations. It is shown that generic deformations do not preserve the known superfield formulations of (2,2) extended supersymmetry. The analysis is performed by decomposing the transformations in terms of the metric vielbein and by introducing space-time connections induced due to the non-linear action of the O(d,d;R) and O(d,d+16;R) deformations on the background fields.