Enhanced Gauge Symmetry in Type II String Theory

TL;DR

This paper explores how singularities in Calabi-Yau compactifications of type II string theory lead to enhanced gauge symmetries, connecting geometric singularities with gauge theories and duality predictions.

Contribution

It demonstrates the emergence of $SU(N)$ gauge theories from geometric singularities and confirms predictions through duality and geometric computations.

Findings

Enhanced gauge symmetry arises from $A_{N-1}$ singularities on Calabi-Yau threefolds.

Massless states are linked to solitons wrapped around collapsing cycles.

Results agree with duality predictions and geometric analyses.

Abstract

We show how enhanced gauge symmetry in type II string theory compactified on a Calabi--Yau threefold arises from singularities in the geometry of the target space. When the target space of the type IIA string acquires a genus $g$ curve $C$ of $A_{N-1}$ singularities, we find that an $SU(N)$ gauge theory with $g$ adjoint hypermultiplets appears at the singularity. The new massless states correspond to solitons wrapped about the collapsing cycles, and their dynamics is described by a twisted supersymmetric gauge theory on $C\times \R^4$. We reproduce this result from an analysis of the $S$-dual $D$-manifold. We check that the predictions made by this model about the nature of the Higgs branch, the monodromy of period integrals, and the asymptotics of the one-loop topological amplitude are in agreement with geometrical computations. In one of our examples we find that the singularity occurs at strong coupling in the heterotic dual proposed by Kachru and Vafa.