Enhanced Gauge Symmetries and K3 Surfaces

TL;DR

This paper investigates enhanced gauge symmetries in type IIA strings on K3 and their relation to orbifold structures, using string-string duality with the heterotic on $T^4$. It shows that classical geometric orbifolds corresponding to enhanced gauge groups need not coincide with conformal field theory orbifolds, due to shifts in the $B$-field moduli, and provides a concrete example via Gepner points where an orbifold CFT has no enhanced gauge symmetry. By analyzing both classical lattices and quantum symmetry extensions, the work demonstrates that the enhanced-gauge locus can be separated from the CFT orbifold point, challenging assumptions about the behavior of the CFT at these loci. The findings highlight the subtle interplay between geometry, $B$-field moduli, and quantum symmetries, with implications for understanding non-perturbative gauge enhancements in string theory.

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.