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 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 New aspects of Argyres-Douglas theories and their dimensional reduction

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Simone Giacomelli ◽  
Noppadol Mekareeya ◽  
Matteo Sacchi
Keyword(s):  
Gauge Theories ◽  
Three Dimensional ◽  
Type I ◽  
Type Ii ◽  
Infinite Class ◽  
Superconformal Field Theories ◽  
Gauge Groups ◽  
Four Dimensions ◽  
Unitary Gauge ◽  
Conformal Manifolds

Abstract Argyres-Douglas (AD) theories constitute an infinite class of superconformal field theories in four dimensions with a number of interesting properties. We study several new aspects of AD theories engineered in A-type class $$ \mathcal{S} $$ S with one irregular puncture of Type I or Type II and also a regular puncture. These include conformal manifolds, structures of the Higgs branch, as well as the three dimensional gauge theories coming from the reduction on a circle. We find that the latter admits a description in terms of a linear quiver with unitary and special unitary gauge groups, along with a number of twisted hypermultiplets. The origin of these twisted hypermultiplets is explained from the four dimensional perspective. We also propose the three dimensional mirror theories for such linear quivers. These provide explicit descriptions of the magnetic quivers of all the AD theories in question in terms of quiver diagrams with unitary gauge groups, together with a collection of free hypermultiplets. A number of quiver gauge theories presented in this paper are new and have not been studied elsewhere in the literature.

scholarly journals Finite-N corrections to the superconformal index of toric quiver gauge theories

2020 ◽  
Vol 2020 (4) ◽  
Author(s):  
Reona Arai ◽  
Shota Fujiwara ◽  
Yosuke Imamura ◽  
Tatsuya Mori
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Gauge Groups ◽  
Superconformal Index

Abstract The superconformal index of quiver gauge theories realized on D3-branes in toric Calabi–Yau cones is investigated. We use the AdS/CFT correspondence and study D3-branes wrapped on supersymmetric cycles. We focus on brane configurations in which a single D3-brane is wrapped on a cycle, and we do not take account of branes with multiple wrapping. We propose a formula that gives finite-$N$ corrections to the index caused by such brane configurations. We compare the predictions of the formula for several examples with the results on the gauge theory side obtained by using localization for small sizes of gauge groups, and confirm that the formula correctly reproduces the finite-$N$ corrections up to the expected order.

scholarly journals Non-invertible global symmetries and completeness of the spectrum

2021 ◽  
Vol 2021 (9) ◽  
Author(s):  
Ben Heidenreich ◽  
Jacob McNamara ◽  
Miguel Montero ◽  
Matthew Reece ◽  
Tom Rudelius ◽  
...  
Keyword(s):  
Gauge Theories ◽  
Cosmic Strings ◽  
Global Symmetry ◽  
Complete Spectrum ◽  
Abelian Gauge ◽  
Analogous Statement ◽  
Gauge Groups ◽  
Four Dimensions ◽  
Chern Simons ◽  
General Gauge

Abstract It is widely believed that consistent theories of quantum gravity satisfy two basic kinematic constraints: they are free from any global symmetry, and they contain a complete spectrum of gauge charges. For compact, abelian gauge groups, completeness follows from the absence of a 1-form global symmetry. However, this correspondence breaks down for more general gauge groups, where the breaking of the 1-form symmetry is insufficient to guarantee a complete spectrum. We show that the correspondence may be restored by broadening our notion of symmetry to include non-invertible topological operators, and prove that their absence is sufficient to guarantee a complete spectrum for any compact, possibly disconnected gauge group. In addition, we prove an analogous statement regarding the completeness of twist vortices: codimension-2 objects defined by a discrete holonomy around their worldvolume, such as cosmic strings in four dimensions. We discuss how this correspondence is modified in various, more general contexts, including non-compact gauge groups, Higgsing of gauge theories, and the addition of Chern-Simons terms. Finally, we discuss the implications of our results for the Swampland program, as well as the phenomenological implications of the existence of twist strings.

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
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