Dilogarithms, OPE and twisted T-duality

TL;DR

This paper investigates the sigma model on the Heisenberg nilmanifold using double field theory, revealing T-duality as a symmetry and uncovering dilogarithmic singularities in correlation functions, with implications for string theory dualities.

Contribution

It demonstrates T-duality as a manifest symmetry in the Hamiltonian formulation of the sigma model on the nilmanifold and links dilogarithm identities to correlation functions.

Findings

Correlation functions exhibit dilogarithmic singularities.

T-duality is a manifest symmetry of the model.

Dilogarithm identities relate to correlator insertions.

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 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.