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Mirror Symmetry in Three-Dimensional Gauge Theories, SL(2,Z) and D-Brane Moduli Spaces

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arxiv hep-th/9612131 v1 pith:TUZTRL2E submitted 1996-12-12 hep-th

Jan de Boer , Kentaro Hori , Hirosi Ooguri , Yaron Oz , Zheng Yin This is my paper · ORCID
classification hep-th
keywords theoriesd-branegaugedualdualitymirrorstringconfigurations
verification ladder T0 review T1 audit T2 compute T3 formal
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We construct intersecting D-brane configurations that encode the gauge groups and field content of dual N=4 supersymmetric gauge theories in three dimensions. The duality which exchanges the Coulomb and Higgs branches and the Fayet-Iliopoulos and mass parameters is derived from the SL(2,Z) symmetry of the type IIB string. Using the D-brane configurations we construct explicitly this mirror map between the dual theories and study the instanton corrections in the D-brane worldvolume theory via open string instantons. A general procedure to obtain mirror pairs is presented and illustrated. We encounter transitions among different field theories that correspond to smooth movements in the D-brane moduli space. We discuss the relation between the duality of the gauge theories and the level-rank duality of affine Lie algebras. Examples of other dual theories are presented and explained via T-duality and extremal transitions in type II string compactifications. Finally we discuss a second way to study instanton corrections in the gauge theory, by wrapping five-branes around six-cycles in M-theory compactified on a Calabi-Yau 4-fold.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Classification of Minimal Abelian Coulomb Branches

    hep-th 2024-12 conditional novelty 7.0 of 10

    Abelian 3d N=4 quivers with isolated Coulomb branch singularities are exactly stable chains and well-defined cycles, with geometries given by U(1) or finite cyclic quotients.

  2. A Tale of Two Orbits: Non-Simply Laced Mirror

    hep-th 2026-05 unverdicted novelty 6.0 of 10

    A 3D N=4 gauge theory is built via U(1) gauging whose Higgs branch matches a known symplectic singularity, with a proposed non-simply laced magnetic quiver mirror validated through standard 3D mirror symmetry tests.

  3. 3d $\mathcal{N}=4$ Mirror Symmetry, TQFTs, and 't Hooft Anomaly Matching

    hep-th 2024-12 conditional novelty 6.0 of 10

    Universal mass deformations of 3d N=4 Abelian gauge theories flow to Abelian spin Chern-Simons TQFTs, with mirror symmetry descending to proven level-rank dualities and 't Hooft anomalies matched via vison fractionalization.

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