The Duality Symmetric String at Two-loops

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.