scholarly journals A-D-E QUIVERS AND BARYONIC OPERATORS

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2285-2286 ◽  
Author(s):  
YUJI TACHIKAWA ◽  
FUTOSHI YAGI
Keyword(s):  
Gauge Theory ◽  
String Theory ◽  
Fixed Points ◽  
Discrete Subgroup ◽  
Theory Analysis ◽  
Gauge Groups ◽  
Quiver Gauge Theory ◽  
Dynkin Diagrams

We study baryonic operators of the gauge theory on multiple D3-branes at the tip of the conifold orbifolded by a discrete subgroup of SU(2). The string theory analysis predicts that the number and the order of the fixed points of this discrete subgroup acting on S2 are directly reflected in the spectrum of baryonic operators on the corresponding quiver gauge theory constructed from two Dynkin diagrams of the corresponding type. We confirm the prediction by utilizing techniques to enumerate baryonic operators of the quiver gauge theory which includes the gauge groups with different ranks.

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.

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 ON THE EXISTENCE OF NONTRIVIAL FIXED POINTS IN LARGE-N GAUGE THEORY IN MORE THAN FOUR DIMENSIONS

1996 ◽  
Vol 11 (39n40) ◽  
pp. 3049-3060 ◽  
Author(s):  
JUN NISHIMURA
Keyword(s):  
Phase Diagram ◽  
Monte Carlo Simulation ◽  
Monte Carlo ◽  
Gauge Theory ◽  
String Theory ◽  
Fixed Points ◽  
Coupling Constants ◽  
Four Dimensions ◽  
Large N ◽  
Six Dimensions

Inspired by a possible relation between large-N gauge theory and string theory, we search for nontrivial fixed points in large-N gauge theory in more than four dimensions. We study large-N gauge theory through Monte–Carlo simulation of the twisted Eguchi–Kawai model in six dimensions as well as in four dimensions. The phase diagram of the system with the two coupling constants which correspond to the standard plaquette action and the adjoint term has been explored.

scholarly journals Higher form symmetries of Argyres-Douglas theories

2020 ◽  
Vol 2020 (10) ◽  
Author(s):  
Michele Del Zotto ◽  
Iñaki García Etxebarria ◽  
Saghar S. Hosseini
Keyword(s):  
Gauge Theory ◽  
String Theory ◽  
Fixed Points ◽  
Large Class ◽  
Careful Analysis ◽  
Consistency Check ◽  
Compact Field ◽  
Hypersurface Singularities ◽  
Type Iib String Theory

Abstract We determine the structure of 1-form symmetries for all 4d $$ \mathcal{N} $$ N = 2 theories that have a geometric engineering in terms of type IIB string theory on isolated hypersurface singularities. This is a large class of models, that includes Argyres-Douglas theories and many others. Despite the lack of known gauge theory descriptions for most such theories, we find that the spectrum of 1-form symmetries can be obtained via a careful analysis of the non-commutative behaviour of RR fluxes at infinity in the IIB setup. The final result admits a very compact field theoretical reformulation in terms of the BPS quiver. We illustrate our methods in detail in the case of the ($$ \mathfrak{g},{\mathfrak{g}}^{\prime } $$ g , g ′ ) Argyres-Douglas theories found by Cecotti-Neitzke-Vafa. In those cases where $$ \mathcal{N} $$ N = 1 gauge theory descriptions have been proposed for theories within this class, we find agreement between the 1-form symmetries of such $$ \mathcal{N} $$ N = 1 Lagrangian flows and those of the actual Argyres-Douglas fixed points, thus giving a consistency check for these proposals.

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 The ABCDEFG of little strings

2021 ◽  
Vol 2021 (6) ◽  
Author(s):  
Nathan Haouzi ◽  
Can Kozçaz
Keyword(s):  
Gauge Theory ◽  
Partition Function ◽  
Coulomb Gas ◽  
Conformal Block ◽  
Coulomb Branch ◽  
Quiver Gauge Theory ◽  
Codimension Two ◽  
Type Iib String Theory ◽  
Unified Description ◽  
Formula Type

Abstract Starting from type IIB string theory on an ADE singularity, the (2, 0) little string arises when one takes the string coupling gs to 0. In this setup, we give a unified description of the codimension-two defects of the little string, labeled by a simple Lie algebra $$ \mathfrak{g} $$ g . Geometrically, these are D5 branes wrapping 2-cycles of the singularity, subject to a certain folding operation when the algebra is non simply-laced. Equivalently, the defects are specified by a certain set of weights of $$ {}^L\mathfrak{g} $$ L g , the Langlands dual of $$ \mathfrak{g} $$ g . As a first application, we show that the instanton partition function of the $$ \mathfrak{g} $$ g -type quiver gauge theory on the defect is equal to a 3-point conformal block of the $$ \mathfrak{g} $$ g -type deformed Toda theory in the Coulomb gas formalism. As a second application, we argue that in the (2, 0) CFT limit, the Coulomb branch of the defects flows to a nilpotent orbit of $$ \mathfrak{g} $$ g .

scholarly journals String theory and the mapping of gravity into gauge theory

2003 ◽  
Vol 560 (1-2) ◽  
pp. 98-107 ◽  
Author(s):  
N.E.J. Bjerrum-Bohr
Keyword(s):  
Gauge Theory ◽  
String Theory

scholarly journals META-STABLE BRANE CONFIGURATIONS WITH MULTIPLE NS5-BRANES

2009 ◽  
Vol 24 (27) ◽  
pp. 5051-5120
Author(s):  
CHANGHYUN AHN
Keyword(s):  
Gauge Theory ◽  
String Theory ◽  
Gauge Group ◽  
Gauge Theories ◽  
The Other ◽  
Multiple Product

Starting from an [Formula: see text] supersymmetric electric gauge theory with the multiple product gauge group and the bifundamentals, 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. Then we describe the intersecting brane configurations, where there are NS-branes and D4-branes (and anti-D4-branes), of type IIA string theory corresponding to the meta-stable nonsupersymmetric vacua of this gauge theory. We also discuss the case where the orientifold 4-planes are added into the above brane configuration. Next, by adding an orientifold 6-plane, we apply to an [Formula: see text] supersymmetric electric gauge theory with the multiple product gauge group (where a single symplectic or orthogonal gauge group is present) and the bifundamentals. Finally, we describe the other cases where the orientifold 6-plane intersects with NS-brane.

scholarly journals Recursive relations for a quiver gauge theory

2006 ◽  
Vol 2006 (10) ◽  
pp. 026-026 ◽  
Author(s):  
Jaemo Park ◽  
Woojoo Sim
Keyword(s):  
Gauge Theory ◽  
Quiver Gauge Theory ◽  
Recursive Relations
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