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 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 The Dyon Charge in Noncommutative Gauge Theories

2008 ◽  
Vol 2008 ◽  
pp. 1-4 ◽  
Author(s):  
L. Cieri ◽  
F. A. Schaposnik
Keyword(s):  
Gauge Theory ◽  
Cp Violation ◽  
Gauge Theories ◽  
Higgs Model ◽  
Ordinary Space ◽  
Yang Mills ◽  
Noncommutative Version ◽  
Noncommutative Gauge Theory ◽  
Noncommutative Gauge Theories

We construct a dyon solution for the noncommutative version of the Yang-Mills-Higgs model with a ϑ-term. Extending the Noether method to the case of a noncommutative gauge theory, we analyze the effect of CP violation induced both by the ϑ-term and by noncommutativity proving that the Witten effect formula for the dyon charge remains the same as in ordinary space.

scholarly journals ANOMALIES IN NONCOMMUTATIVE GAUGE THEORIES, SEIBERG–WITTEN TRANSFORMATION AND RAMOND–RAMOND COUPLINGS

2004 ◽  
Vol 19 (04) ◽  
pp. 613-630 ◽  
Author(s):  
RABIN BANERJEE
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Chern Character ◽  
Exact Expression ◽  
Gauge Invariant ◽  
Axial Anomaly ◽  
Noncommutative Gauge Theory ◽  
Noncommutative Gauge Theories

We propose an exact expression for the unintegrated form of the star gauge-invariant axial anomaly in an arbitrary even dimensional noncommutative gauge theory. The proposal is based on our earlier work,7 as well as on the inverse Seiberg–Witten map and identities related to it, obtained previously15,18 by comparing Ramond–Ramond couplings in different descriptions. The integrated anomalies, found from the unintegrated ones, are expressed in terms of a simplified version of the Elliott formula involving the noncommutative Chern character. These anomalies, under the Seiberg–Witten transformation, reduce to the ordinary (integrated) axial anomalies. Compatibility with existing results of anomalies in noncommutative theories is established.

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 ON THE ANOMALIES AND SCHWINGER TERMS IN NONCOMMUTATIVE GAUGE THEORIES

2006 ◽  
Vol 21 (19n20) ◽  
pp. 4161-4183 ◽  
Author(s):  
F. ARDALAN ◽  
H. ARFAEI ◽  
N. SADOOGHI
Keyword(s):  
Gauge Theory ◽  
Current Algebra ◽  
Gauge Theories ◽  
Noncommutative Gauge Theories

Invariant (nonplanar) anomaly of noncommutative QED is reexamined in this paper. It is found that just as in ordinary gauge theory UV regularization is needed to discover anomalies, in noncommutative case, in addition, an IR regularization is also required to exhibit the existence of invariant anomaly. Thus resolving the controversy in the value of invariant anomaly, an expression for the unintegrated anomaly is found. Schwinger terms of the current algebra of the theory are derived.

scholarly journals Four-dimensional noncommutative deformations of U(1) gauge theory and L∞ bootstrap.

2022 ◽  
Vol 2022 (1) ◽  
Author(s):  
Maxim Kurkov ◽  
Patrizia Vitale
Keyword(s):  
Gauge Theory ◽  
Field Strength ◽  
Gauge Theories ◽  
General Scheme ◽  
Three Dimensional ◽  
Theoretical Models ◽  
Classical Action ◽  
Gauge Transformations ◽  
Noncommutative Algebras ◽  
Noncommutative Gauge Theories

Abstract We construct a family of four-dimensional noncommutative deformations of U(1) gauge theory following a general scheme, recently proposed in JHEP 08 (2020) 041 for a class of coordinate-dependent noncommutative algebras. This class includes the $$ \mathfrak{su} $$ su (2), the $$ \mathfrak{su} $$ su (1, 1) and the angular (or λ-Minkowski) noncommutative structures. We find that the presence of a fourth, commutative coordinate x0 leads to substantial novelties in the expression for the deformed field strength with respect to the corresponding three-dimensional case. The constructed field theoretical models are Poisson gauge theories, which correspond to the semi-classical limit of fully noncommutative gauge theories. Our expressions for the deformed gauge transformations, the deformed field strength and the deformed classical action exhibit flat commutative limits and they are exact in the sense that all orders in the deformation parameter are present. We review the connection of the formalism with the L∞ bootstrap and with symplectic embeddings, and derive the L∞-algebra, which underlies our model.

scholarly journals PLANAR AND NONPLANAR KONISHI ANOMALIES AND EFFECTIVE SUPERPOTENTIAL FOR NONCOMMUTATIVE ${\mathcal N}=1$ SUPERSYMMETRIC U(1)

2005 ◽  
Vol 20 (13) ◽  
pp. 2859-2892 ◽  
Author(s):  
FARHAD ARDALAN ◽  
NÉDA SADOOGHI
Keyword(s):  
Gauge Theory ◽  
Gauge Field ◽  
Gauge Theories ◽  
Gauge Invariant ◽  
Noncommutative Gauge Theories

The Konishi anomalies for noncommutative [Formula: see text] supersymmetric U (1) gauge theory arising from planar and nonplanar diagrams are calculated. Whereas planar Konishi anomaly is the expected ⋆-deformation of the commutative anomaly, nonplanar anomaly reflects the important features of nonplanar diagrams of noncommutative gauge theories, such as UV/IR mixing and the appearance of nonlocal open Wilson lines. We use the planar and nonplanar Konishi anomalies to calculate the effective superpotential of the theory. In the limit of vanishing |Θp|, with Θ the noncommutativity parameter, the noncommutative effective superpotential depends on a gauge invariant superfield, which includes supersymmetric Wilson lines, and has nontrivial dependence on the gauge field supermultiplet.

scholarly journals Abelian p-form (p = 1, 2, 3) gauge theories as the field theoretic models for the Hodge theory

2014 ◽  
Vol 29 (24) ◽  
pp. 1450135 ◽  
Author(s):  
R. Kumar ◽  
S. Krishna ◽  
A. Shukla ◽  
R. P. Malik
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Hodge Theory ◽  
Space Time ◽  
Continuous Symmetry ◽  
Gauge Transformations ◽  
Perfect Model ◽  
De Rham ◽  
Symmetry Transformations ◽  
Dimensions Of Space

Taking the simple examples of an Abelian 1-form gauge theory in two (1+1)-dimensions, a 2-form gauge theory in four (3+1)-dimensions and a 3-form gauge theory in six (5+1)-dimensions of space–time, we establish that such gauge theories respect, in addition to the gauge symmetry transformations that are generated by the first-class constraints of the theory, additional continuous symmetry transformations. We christen the latter symmetry transformations as the dual-gauge transformations. We generalize the above gauge and dual-gauge transformations to obtain the proper (anti-)BRST and (anti-)dual-BRST transformations for the Abelian 3-form gauge theory within the framework of BRST formalism. We concisely mention such symmetries for the 2D free Abelian 1-form and 4D free Abelian 2-form gauge theories and briefly discuss their topological aspects in our present endeavor. We conjecture that any arbitrary Abelian p-form gauge theory would respect the above cited additional symmetry in D = 2p(p = 1, 2, 3, …) dimensions of space–time. By exploiting the above inputs, we establish that the Abelian 3-form gauge theory, in six (5+1)-dimensions of space–time, is a perfect model for the Hodge theory whose discrete and continuous symmetry transformations provide the physical realizations of all aspects of the de Rham cohomological operators of differential geometry. As far as the physical utility of the above nilpotent symmetries is concerned, we demonstrate that the 2D Abelian 1-form gauge theory is a perfect model of a new class of topological theory and 4D Abelian 2-form as well as 6D Abelian 3-form gauge theories are the field theoretic models for the quasi-topological field 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.

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