Two-loop conformal invariance for Yang-Baxter deformed strings

TL;DR

This paper demonstrates that unimodular Yang-Baxter deformations of bosonic strings preserve conformal invariance up to two-loop order by solving corrected supergravity equations and deriving explicit ' corrections, extending the known invariance of TsT transformations.

Contribution

It shows that unimodular YB deformations preserve conformal symmetry to two-loop order and provides explicit ' corrections, extending the understanding of deformation invariance beyond TsT transformations.

Findings

YB deformations solve '-corrected supergravity equations to second order.

Explicit ' corrections for deformed backgrounds are derived.

First ' correction to all orders obtained using '-corrected T-duality rules.

Abstract

The so-called homogeneous Yang-Baxter (YB) deformations can be considered a non-abelian generalization of T-duality--shift--T-duality (TsT) transformations. TsT transformations are known to preserve conformal symmetry to all orders in $\alpha'$. Here we argue that (unimodular) YB deformations of a bosonic string also preserve conformal symmetry, at least to two-loop order. We do this by showing that, starting from a background with no NSNS-flux, the deformed background solves the $\alpha'$-corrected supergravity equations to second order in the deformation parameter. At the same time we determine the required $\alpha'$-corrections of the deformed background, which take a relatively simple form. In examples that can be constructed using, possibly non-commuting sequences of, TsT transformations we show how to obtain the first $\alpha'$-correction to all orders in the deformation parameter by making use of the $\alpha'$-corrected T-duality rules. We demonstrate this on the specific example of YB deformations of a Bianchi type II background.