Enhanced Gauge Symmetries and K3 Surfaces

TL;DR

This paper investigates the nature of enhanced gauge symmetries in type IIA string theory compactified on K3 surfaces, challenging the assumption that such theories are orbifolds and exploring their conformal field theory properties.

Contribution

It demonstrates that theories with enhanced gauge symmetries are not necessarily orbifolds and highlights differences in the B-field, raising questions about their conformal field theory behavior.

Findings

Enhanced gauge symmetries occur without orbifold structure.

The B-field differs between orbifold and non-orbifold theories with the same K3 surface.

Potential issues with the conformal field theory description of these theories.

Abstract

String-string duality dictates that type IIA strings compactified on a K3 surface acquire non-abelian gauge groups for certain values of the K3 moduli. We argue that, contrary to expectation, the theories for which such enhanced gauge symmetries appear are not orbifolds in the string sense. For a specific example we show that a theory with enhanced gauge symmetry and an orbifold theory have the same classical K3 surface as a target space but the value of the ``B-field'' differs. This raises the possibility that the conformal field theory associated to a string theory with an enhanced gauge group is badly behaved in some way.