Conformal Aspects of Spinor-Vector Duality

TL;DR

This paper investigates the origin of Spinor-Vector duality in heterotic string compactifications, linking it to conformal field theory structures, spectral flow, and underlying superconformal theories, revealing continuous interpolations and new symmetries.

Contribution

It uncovers the conformal field theory basis of Spinor-Vector duality and demonstrates how spectral flow and current algebra representations underpin this duality in string models.

Findings

Duality arises from spectral flow in twisted sectors.

Continuous interpolation between dual vacua in N=2 models.

Identification of chiral character identities related to MSDS symmetry.

Abstract

We present a detailed study of various aspects of Spinor-Vector duality in Heterotic string compactifications and expose its origin in terms of the internal conformal field theory. In particular, we illustrate the main features of the duality map by using simple toroidal orbifolds preserving N_4 = 1 and N_4 = 2 spacetime supersymmetries in four dimensions. We explain how the duality map arises in this context by turning on special values of the Wilson lines around the compact cycles of the manifold. We argue that in models with N_4 = 2 spacetime supersymmetry, the interpolation between the Spinor-Vector dual vacua can be continuously realized. We trace the origin of the Spinor-Vector duality map to the presence of underlying N = (2, 2) and N = (4, 4) SCFTs, and explicitly show that the induced spectral-flow in the twisted sectors is responsible for the observed duality. The isomorphism between current algebra representations gives rise to a number of chiral character identities, reminiscent of the recently-discovered MSDS symmetry.