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 ON THE SPACE–TIME SYMMETRIES OF NONCOMMUTATIVE GAUGE THEORIES

2002 ◽  
Vol 17 (17) ◽  
pp. 2369-2376 ◽  
Author(s):  
A. IORIO ◽  
T. SÝKORA
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Space Time ◽  
Time Transformation ◽  
Conformal Transformations ◽  
Gauge Groups ◽  
Noncommutative Gauge Theories

We study the space–time symmetries and transformation properties of the non-commutative U(1) gauge theory, by using Noether charges. We carry out our analysis by keeping an open view on the possible ways θμν could transform. Since the theory is not invariant under the conformal transformations, with the only exception of space–time translations, we conclude that the most natural and dynamically consistent requirement is that θμν does not transform under any space–time transformation. A similar analysis should apply to other gauge groups.

scholarly journals Discrete theta angles, symmetries and anomalies

2021 ◽  
Vol 10 (2) ◽  
Author(s):  
Po-Shen Hsin ◽  
Ho Tat Lam
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Topological Quantum Field Theory ◽  
Group Symmetry ◽  
Global Symmetry ◽  
Quantum Field ◽  
Additional Symmetry ◽  
Gauge Groups ◽  
Topological Quantum ◽  
Symmetry Protected

Gauge theories in various dimensions often admit discrete theta angles, that arise from gauging a global symmetry with an additional symmetry protected topological (SPT) phase. We discuss how the global symmetry and ’t Hooft anomaly depends on the discrete theta angles by coupling the gauge theory to a topological quantum field theory (TQFT). We observe that gauging an Abelian subgroup symmetry, that participates in symmetry extension, with an additional SPT phase leads to a new theory with an emergent Abelian symmetry that also participates in a symmetry extension. The symmetry extension of the gauge theory is controlled by the discrete theta angle which comes from the SPT phase. We find that discrete theta angles can lead to two-group symmetry in 4d4d QCD with SU(N),SU(N)/\mathbb{Z}_kSU(N),SU(N)/ℤk or SO(N)SO(N) gauge groups as well as various 3d3d and 2d2d gauge theories.

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 META-STABLE BRANE CONFIGURATIONS OF TRIPLE PRODUCT GAUGE GROUPS

2009 ◽  
Vol 24 (25n26) ◽  
pp. 4869-4922
Author(s):  
CHANGHYUN AHN
Keyword(s):  
Gauge Theory ◽  
String Theory ◽  
Gauge Group ◽  
Gauge Theories ◽  
Triple Product ◽  
Gauge Groups ◽  
Multiple Product

From an [Formula: see text] supersymmetric electric gauge theory with the gauge group [Formula: see text] with fundamentals for each gauge group and the bifundamentals, we apply Seiberg dual to each gauge group and obtain the [Formula: see text] supersymmetric dual magnetic gauge theories with dual matters including the additional gauge singlets. By analyzing the F-term equations of the dual magnetic superpotentials, we describe the intersecting brane configurations of type IIA string theory corresponding to the meta-stable nonsupersymmetric vacua of this gauge theory. We apply also to the case for [Formula: see text] supersymmetric electric gauge theory with the gauge group [Formula: see text] with flavors for each gauge group and the bifundamentals. Finally, we describe the meta-stable brane configurations of multiple product gauge groups.

scholarly journals META-STABLE BRANE CONFIGURATIONS OF MULTIPLE PRODUCT GAUGE GROUPS WITH ORIENTIFOLD 6 PLANE

2009 ◽  
Vol 24 (25n26) ◽  
pp. 4805-4868
Author(s):  
CHANGHYUN AHN
Keyword(s):  
Gauge Theory ◽  
String Theory ◽  
Gauge Group ◽  
Gauge Theories ◽  
Gauge Groups ◽  
Multiple Product

Starting from an [Formula: see text] supersymmetric electric gauge theory with the gauge group [Formula: see text] with fundamentals for each gauge group, the bifundamentals, a symmetric flavor and a conjugate symmetric flavor for SU (Nc), we apply Seiberg dual to each gauge group, obtain the [Formula: see text] supersymmetric dual magnetic gauge theories with dual matters including the gauge singlets, and describe the intersecting brane configurations of type IIA string theory corresponding to the meta-stable nonsupersymmetric vacua of this gauge theory. We also discuss the case where a symmetric flavor is replaced by an antisymmetric flavor. Next we apply to the case for [Formula: see text] supersymmetric electric gauge theory with the gauge group [Formula: see text] with flavors for each gauge group and the bifundamentals. Finally, we describe the case where the orientifold 6-plane charge is reversed.

scholarly journals Notes on two-dimensional pure supersymmetric gauge theories

2021 ◽  
Vol 2021 (4) ◽  
Author(s):  
Wei Gu ◽  
Eric Sharpe ◽  
Hao Zou
Keyword(s):  
Gauge Theory ◽  
Degrees Of Freedom ◽  
Gauge Theories ◽  
Universal Covering ◽  
Chiral Multiplet ◽  
Two Dimensional ◽  
Supersymmetric Gauge Theories ◽  
Gauge Groups ◽  
Pure Gauge ◽  
Supersymmetric Gauge

Abstract In this note we study IR limits of pure two-dimensional supersymmetric gauge theories with semisimple non-simply-connected gauge groups including SU(k)/ℤk, SO(2k)/ℤ2, Sp(2k)/ℤ2, E6/ℤ3, and E7/ℤ2 for various discrete theta angles, both directly in the gauge theory and also in nonabelian mirrors, extending a classification begun in previous work. We find in each case that there are supersymmetric vacua for precisely one value of the discrete theta angle, and no supersymmetric vacua for other values, hence supersymmetry is broken in the IR for most discrete theta angles. Furthermore, for the one distinguished value of the discrete theta angle for which supersymmetry is unbroken, the theory has as many twisted chiral multiplet degrees of freedom in the IR as the rank. We take this opportunity to further develop the technology of nonabelian mirrors to discuss how the mirror to a G gauge theory differs from the mirror to a G/K gauge theory for K a subgroup of the center of G. In particular, the discrete theta angles in these cases are considerably more intricate than those of the pure gauge theories studied in previous papers, so we discuss the realization of these more complex discrete theta angles in the mirror construction. We find that discrete theta angles, both in the original gauge theory and their mirrors, are intimately related to the description of centers of universal covering groups as quotients of weight lattices by root sublattices. We perform numerous consistency checks, comparing results against basic group-theoretic relations as well as with decomposition, which describes how two-dimensional theories with one-form symmetries (such as pure gauge theories with nontrivial centers) decompose into disjoint unions, in this case of pure gauge theories with quotiented gauge groups and discrete theta angles.

scholarly journals A 4d $$ \mathcal{N} $$ = 1 Cardy Formula

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Joonho Kim ◽  
Seok Kim ◽  
Jaewon Song
Keyword(s):  
Black Holes ◽  
Free Energy ◽  
Asymptotic Behavior ◽  
High Temperature ◽  
Gauge Theory ◽  
Chemical Potential ◽  
Temperature Limit ◽  
Superconformal Index ◽  
High Temperature Limit ◽  
Cardy Formula

Abstract We study the asymptotic behavior of the (modified) superconformal index for 4d $$ \mathcal{N} $$ N = 1 gauge theory. By considering complexified chemical potential, we find that the ‘high-temperature limit’ of the index can be written in terms of the conformal anomalies 3c − 2a. We also find macroscopic entropy from our asymptotic free energy when the Hofman-Maldacena bound 1/2 < a/c < 3/2 for the interacting SCFT is satisfied. We study $$ \mathcal{N} $$ N = 1 theories that are dual to AdS5 × Yp,p and find that the Cardy limit of our index accounts for the Bekenstein-Hawking entropy of large black holes.

scholarly journals The Volume of the Quiver Vortex Moduli Space

2021 ◽  
Author(s):  
Kazutoshi Ohta ◽  
Norisuke Sakai
Keyword(s):  
Gauge Theory ◽  
Moduli Space ◽  
Riemann Surfaces ◽  
Gauge Theories ◽  
Target Space ◽  
Contour Integral ◽  
Quiver Gauge Theory ◽  
Volume Formula ◽  
Volume Operator ◽  
Space Volume

Abstract We study the moduli space volume of BPS vortices in quiver gauge theories on compact Riemann surfaces. The existence of BPS vortices imposes constraints on the quiver gauge theories. We show that the moduli space volume is given by a vev of a suitable cohomological operator (volume operator) in a supersymmetric quiver gauge theory, where BPS equations of the vortices are embedded. In the supersymmetric gauge theory, the moduli space volume is exactly evaluated as a contour integral by using the localization. Graph theory is useful to construct the supersymmetric quiver gauge theory and to derive the volume formula. The contour integral formula of the volume (generalization of the Jeffrey-Kirwan residue formula) leads to the Bradlow bounds (upper bounds on the vorticity by the area of the Riemann surface divided by the intrinsic size of the vortex). We give some examples of various quiver gauge theories and discuss properties of the moduli space volume in these theories. Our formula are applied to the volume of the vortex moduli space in the gauged non-linear sigma model with CPN target space, which is obtained by a strong coupling limit of a parent quiver gauge theory. We also discuss a non-Abelian generalization of the quiver gauge theory and “Abelianization” of the volume formula.

scholarly journals Seiberg-like dualities for orthogonal and symplectic 3d $$ \mathcal{N} $$ = 2 gauge theories with boundaries

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Tadashi Okazaki ◽  
Douglas J. Smith
Keyword(s):  
Boundary Conditions ◽  
Gauge Theories ◽  
Gauge Groups

Abstract We propose dualities of $$ \mathcal{N} $$ N = (0, 2) supersymmetric boundary conditions for 3d $$ \mathcal{N} $$ N = 2 gauge theories with orthogonal and symplectic gauge groups. We show that the boundary ’t Hooft anomalies and half-indices perfectly match for each pair of the proposed dual boundary conditions.

scholarly journals On the quantization of Seiberg-Witten geometry

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Nathan Haouzi ◽  
Jihwan Oh
Keyword(s):  
Gauge Theory ◽  
String Theory ◽  
Partition Function ◽  
Flat Space ◽  
Matter Content ◽  
Gauge Groups ◽  
Space Limit ◽  
Two Parameters ◽  
Double Quantization ◽  
Quantization Parameters

Abstract We propose a double quantization of four-dimensional $$ \mathcal{N} $$ N = 2 Seiberg-Witten geometry, for all classical gauge groups and a wide variety of matter content. This can be understood as a set of certain non-perturbative Schwinger-Dyson identities, following the program initiated by Nekrasov [1]. The construction relies on the computation of the instanton partition function of the gauge theory on the so-called Ω-background on ℝ4, in the presence of half-BPS codimension 4 defects. The two quantization parameters are identified as the two parameters of this background. The Seiberg-Witten curve of each theory is recovered in the flat space limit. Whenever possible, we motivate our construction from type IIA string theory.

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