The Duality Symmetric String at Two-loops

TL;DR

This paper investigates the two-loop renormalization of the duality symmetric string theory in cosmological spacetimes, revealing that counter-terms break $O(n,n)$ symmetry and challenge the model's renormalizability.

Contribution

It provides a detailed two-loop analysis of the Tseytlin duality symmetric string, highlighting issues with $O(n,n)$ symmetry preservation during renormalization.

Findings

Two-loop counter-terms break $O(n,n)$ symmetry.

Renormalizability of the duality symmetric string is obstructed.

Different methods are used to handle complex loop integrals.

Abstract

The Tseytlin duality symmetric string makes manifest the $O(n,n)$ T-duality symmetry on the worldsheet at the expense of manifest Lorentz invariance. Here we consider the two-loop renormalisation of this model in the context of "cosmological" spacetimes consisting of an internal $n$-dimensional torus fibred over a one-dimensional base manifold. The lack of manifest Lorentz symmetry introduces a range of complexities in momenta loop integrals which we approach using different methods. Whilst the results do satisfy a number of key consistency criteria, we find however that the two-loop counter-terms are incompatible with $O(n,n)$ symmetry and obstruct the renormalisability of the duality symmetric string.