scholarly journals Mirror symmetry and toric geometry in three-dimensional gauge theories

2000 ◽  
Vol 2000 (05) ◽  
pp. 018-018 ◽  
Author(s):  
Nick Dorey ◽  
David Tong
Keyword(s):  
Mirror Symmetry ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Toric Geometry

scholarly journals A string theory realization of special unitary quivers in 3 dimensions

2020 ◽  
Vol 2020 (11) ◽  
Author(s):  
Andrés Collinucci ◽  
Roberto Valandro
Keyword(s):  
String Theory ◽  
Mirror Symmetry ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Holomorphic Curves ◽  
Gauge Groups ◽  
Unitary Gauge

Abstract We propose a string theory realization of three-dimensional $$ \mathcal{N} $$ N = 4 quiver gauge theories with special unitary gauge groups. This is most easily understood in type IIA string theory with D4-branes wrapped on holomorphic curves in local K3’s, by invoking the Stückelberg mechanism. From the type IIB perspective, this is understood as simply compactifying the familiar Hanany-Witten (HW) constructions on a T3. The mirror symmetry duals are easily derived. We illustrate this with various examples of mirror pairs.

scholarly journals M-theory origin of mirror symmetry in three-dimensional gauge theories

1997 ◽  
Vol 490 (1-2) ◽  
pp. 107-120 ◽  
Author(s):  
Massimo Porrati ◽  
Alberto Zaffaroni
Keyword(s):  
Mirror Symmetry ◽  
Gauge Theories ◽  
Three Dimensional ◽  
M Theory

scholarly journals Connecting mirror symmetry in 3D and 2D via localization

2014 ◽  
Vol 29 (32) ◽  
pp. 1530004 ◽  
Author(s):  
Heng-Yu Chen ◽  
Hsiao-Yi Chen ◽  
Jun-Kai Ho
Keyword(s):  
Mirror Symmetry ◽  
Gauge Theories ◽  
Three Dimensional ◽  
High Energy ◽  
Partition Functions ◽  
Two Dimensional ◽  
Abelian Gauge ◽  
Fusion Procedure ◽  
Mirror Pair ◽  
Simple Limit

We explicitly apply localization results to study the interpolation between three- and two-dimensional mirror symmetries for Abelian gauge theories with four supercharges. We first use the ellipsoid [Formula: see text] partition functions to verify the mirror symmetry between a pair of general three-dimensional 𝒩 = 2 Abelian Chern–Simons quiver gauge theories. These expressions readily factorize into holomorphic blocks and their antiholomorphic copies, so we can also obtain the partition functions on S1×S2 via fusion procedure. We then demonstrate S1×S2 partition functions for the three-dimensional Abelian gauge theories can be dimensionally reduced to the S2 partition functions of 𝒩 = (2, 2) GLSM and Landau–Ginzburg model for the corresponding two-dimensional mirror pair, as anticipated previously in M. Aganagic et al., J. High Energy Phys.0107, 022 (2001). We also comment on the analogous interpolation for the non-Abelian gauge theories and compute the K-theory vortex partition function for a simple limit to verify the prediction from holomorphic block.

scholarly journals On mirror symmetry in three dimensional Abelian gauge theories

1999 ◽  
Vol 1999 (04) ◽  
pp. 021-021 ◽  
Author(s):  
Anton Kapustin ◽  
Matthew J Strassler
Keyword(s):  
Mirror Symmetry ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Abelian Gauge

scholarly journals Mirror symmetry in three-dimensional gauge theories, quivers and D-branes

1997 ◽  
Vol 493 (1-2) ◽  
pp. 101-147 ◽  
Author(s):  
Jan de Boer ◽  
Kentaro Hori ◽  
Hirosi Ooguri ◽  
Yaron Oz
Keyword(s):  
Mirror Symmetry ◽  
Gauge Theories ◽  
Three Dimensional

scholarly journals Mirror symmetry in three-dimensional gauge theories, and D-brane moduli spaces

1997 ◽  
Vol 493 (1-2) ◽  
pp. 148-176 ◽  
Author(s):  
Jan de Boer ◽  
Kentaro Hori ◽  
Hirosi Ooguri ◽  
Yaron Oz ◽  
Zheng Yin
Keyword(s):  
Moduli Spaces ◽  
Mirror Symmetry ◽  
Gauge Theories ◽  
Three Dimensional

scholarly journals Mirror symmetry in three dimensional gauge theories

1996 ◽  
Vol 387 (3) ◽  
pp. 513-519 ◽  
Author(s):  
K. Intriligator ◽  
N. Seiberg
Keyword(s):  
Mirror Symmetry ◽  
Gauge Theories ◽  
Three Dimensional

scholarly journals Three dimensional mirror symmetry beyond ADE quivers and Argyres-Douglas theories

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Anindya Dey
Keyword(s):  
Mirror Symmetry ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Dual Pair ◽  
Global Symmetry ◽  
Gauge Groups ◽  
Superconformal Index ◽  
Unitary Gauge ◽  
Simple Realization ◽  
Systematic Field

Abstract Mirror symmetry, a three dimensional $$ \mathcal{N} $$ N = 4 IR duality, has been studied in detail for quiver gauge theories of the ADE-type (as well as their affine versions) with unitary gauge groups. The A-type quivers (also known as linear quivers) and the associated mirror dualities have a particularly simple realization in terms of a Type IIB system of D3-D5-NS5-branes. In this paper, we present a systematic field theory prescription for constructing 3d mirror pairs beyond the ADE quiver gauge theories, starting from a dual pair of A-type quivers with unitary gauge groups. The construction involves a certain generalization of the S and the T operations, which arise in the context of the SL(2, ℤ) action on a 3d CFT with a U(1) 0-form global symmetry. We implement this construction in terms of two supersymmetric observables — the round sphere partition function and the superconformal index on S2 × S1. We discuss explicit examples of various (non-ADE) infinite families of mirror pairs that can be obtained in this fashion. In addition, we use the above construction to conjecture explicit 3d $$ \mathcal{N} $$ N = 4 Lagrangians for 3d SCFTs, which arise in the deep IR limit of certain Argyres-Douglas theories compactified on a circle.

scholarly journals Wilson loop algebras and quantum K-theory for Grassmannians

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Hans Jockers ◽  
Peter Mayr ◽  
Urmi Ninad ◽  
Alexander Tabler
Keyword(s):  
Wilson Loop ◽  
Gauge Theories ◽  
Wilson Line ◽  
Quantum Cohomology ◽  
Three Dimensional ◽  
Loop Algebra ◽  
Loop Algebras ◽  
Verlinde Algebra ◽  
K Theory ◽  
Chern Simons

Abstract We study the algebra of Wilson line operators in three-dimensional $$ \mathcal{N} $$ N = 2 supersymmetric U(M ) gauge theories with a Higgs phase related to a complex Grassmannian Gr(M, N ), and its connection to K-theoretic Gromov-Witten invariants for Gr(M, N ). For different Chern-Simons levels, the Wilson loop algebra realizes either the quantum cohomology of Gr(M, N ), isomorphic to the Verlinde algebra for U(M ), or the quantum K-theoretic ring of Schubert structure sheaves studied by mathematicians, or closely related algebras.

scholarly journals Three-dimensional 𝒩 = 2 supersymmetric gauge theories and partition functions on Seifert manifolds: A review

2019 ◽  
Vol 34 (23) ◽  
pp. 1930011 ◽  
Author(s):  
Cyril Closset ◽  
Heeyeon Kim
Keyword(s):  
Correlation Functions ◽  
Gauge Theories ◽  
Three Dimensional ◽  
Partition Functions ◽  
Exact Results ◽  
Strongly Coupled ◽  
Seifert Manifolds ◽  
Recent Developments ◽  
Supersymmetric Gauge ◽  
Chern Simons

We give a pedagogical introduction to the study of supersymmetric partition functions of 3D [Formula: see text] supersymmetric Chern–Simons-matter theories (with an [Formula: see text]-symmetry) on half-BPS closed three-manifolds — including [Formula: see text], [Formula: see text], and any Seifert three-manifold. Three-dimensional gauge theories can flow to nontrivial fixed points in the infrared. In the presence of 3D [Formula: see text] supersymmetry, many exact results are known about the strongly-coupled infrared, due in good part to powerful localization techniques. We review some of these techniques and emphasize some more recent developments, which provide a simple and comprehensive formalism for the exact computation of half-BPS observables on closed three-manifolds (partition functions and correlation functions of line operators). Along the way, we also review simple examples of 3D infrared dualities. The computation of supersymmetric partition functions provides exceedingly precise tests of these dualities.

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