Uncovering a Spinor-Vector Duality on a Resolved Orbifold

TL;DR

This paper explores the existence of spinor-vector dualities in smooth geometries within heterotic string theory, using the resolution of T4/Z2 orbifold with Wilson lines to demonstrate how dualities manifest beyond orbifold limits.

Contribution

It investigates spinor-vector dualities on smooth geometries, specifically through the resolution of orbifolds with Wilson lines, revealing differences in spectra and gauge groups.

Findings

Dualities depend on discrete torsion phases.

Different blowup modes lead to distinct spectra.

Gauge groups differ between dual pairs.

Abstract

Spinor-vector dualities have been established in various exact string realisations like orbifold and free fermionic constructions. This paper aims to investigate possibility of having spinor-vector dualities on smooth geometries in the context of the heterotic string. As a concrete working example the resolution of the T4/Z2 orbifold is considered with an additional circle supporting a Wilson line, for which it is known that the underlying orbifold theory exhibits such a duality by switching on/off a generalised discrete torsion phase between the orbifold twist and the Wilson line. Depending on this phase complementary parts of the twisted sector orbifold states are projected out, so that different blowup modes are available to generate the resolutions. As a consequence, not only the spectra of the dual pairs are different, but also the gauge groups are not identical making this duality less apparent on the blowup and thus presumably on smooth geometries in general.