Dilogarithms, OPE, and Twisted T-Duality

Abstract

We study the full sigma model with target the three-dimensional Heisenberg nilmanifold by means of a Hamiltonian formulation of double field theory. We show that the expected T-duality with the sigma model on a torus endowed with H-flux is a manifest symmetry of the theory. We compute 4-point functions of scalar fields and show that they exhibit dilogarithmic singularities. We show how the reflection and pentagonal identities of the dilogarithm can be interpreted in terms of 4-point functions and 5-point functions.