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Enhanced gauge symmetry in type II string theory. (English) Zbl 0925.81188
Summary: 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 \(C\times \mathbb{R}^{4}\). 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.

MSC:
81T30 String and superstring theories; other extended objects (e.g., branes) in quantum field theory
32J81 Applications of compact analytic spaces to the sciences
32S30 Deformations of complex singularities; vanishing cycles
83E30 String and superstring theories in gravitational theory
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