Background Field Equations for the Duality Symmetric String

TL;DR

This work derives the one-loop background-field equations for the duality-symmetric, or doubled, string by performing a covariant background-field expansion in a formalism where the fibre target space is doubled and constrained via a chirality condition. The authors compute the Weyl divergence (beta-functions) for the doubled geometry and show that, after integrating out the dual coordinates with the constraint, the resulting divergences reproduce the standard beta-functions for the non-doubled metric and B-field, $\beta^G_{\alpha\beta}=R_{\alpha\beta}-\frac{1}{4}H_{\alpha\sigma\delta}H_{\beta}^{\ \sigma\delta}$ and $\beta^B_{\alpha\beta}=-\frac{1}{2}D^{\sigma}H_{\sigma\alpha\beta}$, up to an appropriate mapping of doubled to conventional fields. The L-coupling remains unrenormalised and the potentially problematic Lorentz anomaly cancels between chiral sectors; the topological term does not affect the Weyl analysis. These results establish the quantum equivalence of the doubled and standard string formulations at one loop and pave the way for including the doubled dilaton and higher-loop corrections in this framework, with implications for T-duality and non-geometric backgrounds.

Abstract

This paper describes the background field equations for strings in T-duality symmetric formalisms in which the dimension of target space is doubled and the sigma model supplemented with constraints. These are calculated by demanding the vanishing of the beta-functional of the sigma model couplings in the doubled target space. We demonstrate the equivalence with the background field equations of the standard string sigma model.