Reimundo Helluani
IMPA
Dilogarithms, chiral algebras and non-commutative windings.
Abstract: When studying the movement of free strings on flat Tori from a Hamiltonian perspective, the algebra of observables happens to be a vertex algebra (a lattice vertex algebra in fact, this is just a collection of highest weight representation of an infinite dimensional Heisenberg algebra). When trying to generalize this to other nilmanifolds with non-commutative fundamental group or to their "twisted T-duals", namely flat tori with non-trivial gerbes, one finds a similar structure where the scalar fields have dilogarithmic singularities in their operator product expansion instead of simply logarithms as in the Torus case.