O(d,d) invariance at two and three loops

TL;DR

This paper demonstrates that the O(d,d) invariance of conformal invariance conditions in a specific two-dimensional sigma-model persists at higher loops, specifically at two loops with torsion and at three loops without torsion.

Contribution

It proves the preservation of O(d,d) invariance at two and three loops in a targeted class of sigma-models, extending prior one-loop results.

Findings

O(d,d) invariance holds at two loops with torsion.

O(d,d) invariance holds at three loops without torsion.

The invariance is maintained in models with fields depending on a single target coordinate.

Abstract

We show that in a two-dimensional sigma-model whose fields only depend on one target space co-ordinate, the O(d,d) invariance of the conformal invariance conditions observed at one loop is preserved at two loops (in the general case with torsion) and at three loops (in the case without torsion).