  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 correlation 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 correlators with 4 and 5 insertions.
