Reimundo Heluani

Supersymmetric Vertex Algebras

We define and study the structure of SUSY Lie conformal and vertex algebras. This leads to effective rules for computations with superfields.

Generalized Calabi–Yau manifolds and the chiral de Rham complex

Abstract We show that the chiral de Rham complex of a generalized Calabi–Yau manifold carries N = 2 supersymmetry. We discuss the corresponding topological twist for this N = 2 algebra. We interpret this as an algebroid version of the super-Sugawara or Kac–Todorov construction.

Dilogarithms, OPE, and Twisted T-Duality

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.

SUSY Vertex Algebras and Supercurves

Given a strongly conformal SUSY vertex algebra V and a supercurve X, we construct a vector bundle

Supersymmetry of the chiral de Rham complex

{\fancyscript V}^r_X

Non-linear sigma models via the chiral de Rham complex

on X, the fiber of which is isomorphic to V. Moreover, the state-field correspondence of V canonically gives rise to (local) sections of these vector bundles. We also define chiral algebras on any supercurve X, and show that the vector bundle

Characters of topological N = 2 vertex algebras are Jacobi forms on the moduli space of elliptic supercurves

{\fancyscript V}^r_X