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 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 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 ANOMALY AND NONPLANAR DIAGRAMS IN NONCOMMUTATIVE GAUGE THEORIES

2002 ◽  
Vol 17 (01) ◽  
pp. 123-144 ◽  
Author(s):  
FARHAD ARDALAN ◽  
NÉDA SADOOGHI
Keyword(s):  
Gauge Theory ◽  
Gauge Theories ◽  
Gauge Fields ◽  
Noncommutative Gauge Theory ◽  
Gauge Anomalies ◽  
Noncommutative Gauge Theories ◽  
Matter Fields

Anomalies arising from nonplanar triangle diagrams of noncommutative gauge theory are studied. Local chiral gauge anomalies for both noncommutative U(1) and U(N) gauge theories with adjoint matter fields are shown to vanish. For noncommutative QED with fundamental matters, due to UV/IR mixing a finite anomaly emerges from the nonplanar contributions. It involves a generalized ⋆-product of gauge fields.

scholarly journals DISCRETE NONCOMMUTATIVE GAUGE THEORY

2001 ◽  
Vol 16 (04n06) ◽  
pp. 367-386 ◽  
Author(s):  
RICHARD J. SZABO
Keyword(s):  
Gauge Theory ◽  
Matrix Models ◽  
Wilson Line ◽  
Morita Equivalence ◽  
Generic Properties ◽  
Gauge Invariant ◽  
Fundamental Matter ◽  
Generic Relation ◽  
Noncommutative Gauge Theory ◽  
Noncommutative Quantum

A review of the relationships between matrix models and noncommutative gauge theory is presented. A lattice version of noncommutative Yang–Mills theory is constructed and used to examine some generic properties of noncommutative quantum field theory, such as uv/ir mixing and the appearance of gauge-invariant open Wilson line operators. Morita equivalence in this class of models is derived and used to establish the generic relation between noncommutative gauge theory and twisted reduced models. Finite-dimensional representations of the quotient conditions for toroidal compactification of matrix models are thereby exhibited. The coupling of noncommutative gauge fields to fundamental matter fields is considered and a large mass expansion is used to study the properties of gauge-invariant observables. Morita equivalence with fundamental matter is also presented and used to prove the equivalence between the planar loop renormalizations in commutative and noncommutative quantum chromodynamics.

THE NAMBU-JONA-LASINIO MODEL AND GAUGE THEORIES IN 2+1 DIMENSIONS

1991 ◽  
Vol 06 (04) ◽  
pp. 667-694 ◽  
Author(s):  
K.M. COSTA
Keyword(s):  
Gauge Theory ◽  
Invariant Theory ◽  
Gauge Theories ◽  
Leading Order ◽  
Coupling Constant ◽  
Gauge Invariant ◽  
Strongly Coupled ◽  
Njl Model ◽  
Weakly Coupled ◽  
Bare Coupling Constant

The weakly coupled globally invariant Nambu-Jona-Lasino (NJL) model in 2+1 dimensions is shown to be equivalent to a strongly coupled gauge theory. This equivalence is demonstrated for the renormalized theories in the 1/N expansion utilizing an unconventional, cutoff-dependent bare coupling constant to take the limit of weak or strong bare couplings. The weakly coupled Abelian NJL model is renormalized to order 1/N and compared to a renormalized strongly coupled QED3. Next, the U(2) globally invariant NJL model is studied in the broken phase and renormalized to leading order. The resulting U(1)×U(1) gauge-invariant theory is shown to be equivalent to a spontaneously broken U(2) gauge theory analyzed in the 1/N expansion.

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 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 Holographic Renormalization of Two-Point Functions in Non-AdS/Non-CFT

2010 ◽  
Vol 2010 ◽  
pp. 1-43 ◽  
Author(s):  
Michael Haack ◽  
Wolfgang Mück
Keyword(s):  
Renormalization Group ◽  
Gauge Theory ◽  
Recent Progress ◽  
Gauge Theories ◽  
Gauge Invariant ◽  
Holographic Renormalization ◽  
Invariant Description ◽  
Background Material ◽  
Gauge Gravity

We review recent progress on holographic renormalization in the context of the gauge-gravity correspondence when the bulk geometry is not asymptotically AdS. The prime example is the Klebanov-Strassler background, whose dual gauge theory has logarithmically running couplings at all energy scales. The presented formalism provides the counterterms necessary for obtaining finite two-point functions of the scalar operators in the corresponding dual gauge theories. The presentation is self-contained and reviews all the relevant background material concerning a gauge-invariant description of the fluctuations around holographic renormalization group backgrounds.

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