Nonplanar graphs and anomalies in chiral noncommutative gaugetheories

2005 ◽  
Vol 83 (10) ◽  
pp. 1051-1061 ◽  
Author(s):  
Marie Gagne-Portelance ◽  
D.G.C. McKeon
Keyword(s):  
Gauge Field ◽  
Fermion Field ◽  
Gauge Model ◽  
Surface Term ◽  
Loop Momentum ◽  
Axial Gauge ◽  
Momentum Variable ◽  
Vector Gauge ◽  
Nonplanar Surface

The AV (n) one-loop graphs are examined in a 2n-dimensional massless noncommutative gauge model in which both a U(1) axial gauge field A and a U(1) vector gauge field V have adjoint couplings to a Fermion field. A possible anomaly in the divergence of the n + 1 vertices is examined by considering the surface term that can possibly arise when shifting the loop momentum variable of integration. It is shown that despite the fact that the graphs are nonplanar, surface terms do arise in individual graphs, but that in 4n dimensions, a cancellation between the surface term contribution coming from pairs of graphs eliminates all anomalies, while in 4n + 2 dimensions such a cancellation cannot occur and an anomaly necessarily arises.PACS No.: 11.30.Rd

Several one-loop calculations in a formulation of massive quantum electrodynamics possessing only vacuum-polarization divergences

1985 ◽  
Vol 63 (10) ◽  
pp. 1337-1342
Author(s):  
Stephen Phillips
Keyword(s):  
Gauge Field ◽  
Quantum Electrodynamics ◽  
Explicit Calculation ◽  
Alternative Formulation ◽  
Fermion Field ◽  
Wave Function Renormalization ◽  
Mass Insertion ◽  
Gauge Fixing ◽  
Simple Mass ◽  
Perturbative Quantum

An alternative formulation of path-integral quantization for gauge theories is proposed in which the gauge-fixing condition, normally imposed on just the gauge field itself, is imposed on the gauge-transformed gauge field, a continuous sum now being included over all configurations of the transformation field, Λ(x), that satisfy the gauge condition.It is shown, by explicit calculation, that when bilinear counterterms in the Lagrangian field density are included so as to render the two-point gauge- and fermion-field Green's functions finite, the fermion–fermion–gauge-field Green's function is divergence free. Unlike the more conventional approaches, there is no divergent vertex counterterm needed. Furthermore, the form of the fermion counterterm is a simple mass insertion only. There is no need for a divergent fermion wave-function renormalization. The cancellation of the divergences that are normally present is accomplished by the effect of, heretofor uncommon in perturbative quantum-field theory, infrared-divergent integrals. It is argued heuristically how these may be regulated by the same parameter, Λ, that is used for ultraviolet-divergent integrals, where now the cutoff is towards the lower limit of integration.

scholarly journals SUPER WEYL ANOMALIES IN THE AdS/CFT CORRESPONDENCE

1999 ◽  
Vol 14 (23) ◽  
pp. 3731-3743 ◽  
Author(s):  
MADOKA NISHIMURA ◽  
YOSHIAKI TANII
Keyword(s):  
Central Charge ◽  
Two Dimensions ◽  
Field Theories ◽  
Conformal Supergravity ◽  
Superconformal Field Theories ◽  
Axial Gauge ◽  
Vector Gauge

Anomalies of N=(4,4) superconformal field theories coupled to a conformal supergravity background in two dimensions are computed by using the AdS/CFT correspondence. We find that Weyl, axial gauge and super Weyl transformations are anomalous, while general coordinate, local Lorentz, vector gauge and local supertransformations are not. The coefficients of the anomalies show that the superconformal field theories have the central charge expected in the AdS/CFT correspondence.

TOPOLOGY COLLAPSE OF NONTRIVIAL U(1)-BUNDLE ON LATTICIZED SPHERE

1988 ◽  
Vol 03 (15) ◽  
pp. 1489-1497
Author(s):  
HIROSHI KOIBUCHI ◽  
MITSURU YAMADA
Keyword(s):  
Monte Carlo ◽  
Statistical Mechanics ◽  
Gauge Field ◽  
Low Temperatures ◽  
Field Configuration ◽  
Chern Number ◽  
Monte Carlo Technique ◽  
Metastable States ◽  
Two Dimensional ◽  
Gauge Model

Applying the Monte Carlo technique, we study the statistical mechanics of U(1) gauge model on two dimensional spherical lattice of the Mercator type. Special emphasis is put on the topology of the gauge-field configuration. At sufficiently low temperatures, we demonstrate the existence of many metastable states, each of which has a well-defined Chern number. At higher temperatures, we observe how they lose their topology and collapse.

scholarly journals A new approach to anomalous axial vector field theory

2021 ◽  
pp. 2150104
Author(s):  
A. K. Kapoor
Keyword(s):  
Field Theory ◽  
Axial Vector ◽  
Ultra Violet ◽  
Realistic Model ◽  
Quantization Scheme ◽  
Stochastic Quantization ◽  
Gauge Model ◽  
Operator Formalism ◽  
New Approach ◽  
Vector Gauge

In an earlier paper, it has been shown that the ultra violet divergence structure of anomalous [Formula: see text] axial vector gauge model in the stochastic quantization scheme is different from that in the conventional quantum field theory. Also, it has been shown that the model is expected to be renormalizable. Based on the operator formalism of the stochastic quantization, a new approach to anomalous [Formula: see text] axial vector gauge model is proposed. The operator formalism provides a convenient framework for analysis of ultra violet divergences, but the computations in a realistic model become complicated. In this paper a new approach to do computations in the model is formulated directly in four dimensions. The suggestions put forward here will lead to simplification in the study of applications of the axial vector gauge theory, as well as those of other similar models.

scholarly journals Partition functions of higher derivative conformal fields on conformally related spaces

2021 ◽  
Vol 2021 (10) ◽  
Author(s):  
Jyotirmoy Mukherjee
Keyword(s):  
Partition Function ◽  
Integral Representation ◽  
Gauge Field ◽  
Partition Functions ◽  
Conformal Vector ◽  
Higher Derivative ◽  
Conformal Fields ◽  
Vector Gauge ◽  
Bulk Part ◽  
Hyperbolic Cylinders

Abstract The character integral representation of one loop partition functions is useful to establish the relation between partition functions of conformal fields on Weyl equivalent spaces. The Euclidean space Sa × AdSb can be mapped to Sa+b provided Sa and AdSb are of the same radius. As an example, to begin with, we show that the partition function in the character integral representation of conformally coupled free scalars and fermions are identical on Sa × AdSb and Sa+b. We then demonstrate that the partition function of higher derivative conformal scalars and fermions are also the same on hyperbolic cylinders and branched spheres. The partition function of the four-derivative conformal vector gauge field on the branched sphere in d = 6 dimension can be expressed as an integral over ‘naive’ bulk and ‘naive’ edge characters. However, the partition function of the conformal vector gauge field on $$ {S}_q^1 $$ S q 1 × AdS5 contains only the ‘naive’ bulk part of the partition function. This follows the same pattern which was observed for the partition of conformal p-form fields on hyperbolic cylinders. We use the partition function of higher derivative conformal fields on hyperbolic cylinders to obtain a linear relationship between the Hofman-Maldacena variables which enables us to show that these theories are non-unitary.

COMPOSITE CHERN-SIMONS GAUGE BOSON IN ANYON GAS

1991 ◽  
Vol 05 (01n02) ◽  
pp. 391-401
Author(s):  
NGUYEN VAN HIEU ◽  
NGUYEN HUNG SON
Keyword(s):  
Gauge Field ◽  
Gauge Boson ◽  
Effective Action ◽  
Momentum Dependence ◽  
Composite Boson ◽  
Dispersion Equations ◽  
Vector Gauge ◽  
Chern Simons

It was shown that in a free anyon gas there exists a composite vector gauge field with the effective action containing a Chern-Simons term. The momentum dependence of the energy of the composite boson was found. The mixing between Chern-Simons boson and photon gives rise to the appearance of new quasiparticles -Chern-Simons polaritons. The dispersion equations of Chern-Simons polaritons were derived.

scholarly journals Why is the mission impossible? Decoupling the mirror Ginsparg–Wilson fermions in the lattice models for two-dimensional Abelian chiral gauge theories

2019 ◽  
Vol 2019 (7) ◽  
Author(s):  
Y Kikukawa
Keyword(s):  
Gauge Field ◽  
Strong Coupling ◽  
Vertex Function ◽  
Gauge Theories ◽  
Local Behavior ◽  
Gauge Model ◽  
Locality Property ◽  
Yukawa Couplings ◽  
Point Vertex ◽  
Wilson Fermions

Abstract It is known that the four-dimensional Abelian chiral gauge theories of an anomaly-free set of Wely fermions can be formulated on the lattice preserving the exact gauge invariance and the required locality property in the framework of the Ginsparg–Wilson relation. This holds true in two dimensions. However, in the related formulation including the mirror Ginsparg–Wilson fermions, and therefore having a simpler fermion path-integral measure, it has been argued that the mirror fermions do not decouple: in the 345 model with Dirac– and Majorana–Yukawa couplings to the XY-spin field, the two-point vertex function of the (external) gauge field in the mirror sector shows a singular non-local behavior in the paramagnetic strong-coupling phase. We re-examine why the attempt seems to be a “Mission: Impossible” in the 345 model. We point out that the effective operators to break the fermion number symmetries (‘t Hooft operators plus others) in the mirror sector do not have sufficiently strong couplings even in the limit of large Majorana–Yukawa couplings. We also observe that the type of Majorana–Yukawa term considered is singular in the large limit due to the nature of the chiral projection of the Ginsparg–Wilson fermions, but a slight modification without such a singularity is allowed by virtue of their very nature. We then consider a simpler four-flavor axial gauge model, the $1^4(-1)^4$ model, in which the U(1)$_A$ gauge and Spin(6)(SU(4)) global symmetries prohibit the bilinear terms but allow the quartic terms to break all the other continuous mirror fermion symmetries. We formulate the model so that it is well behaved and simplified in the strong-coupling limit of the quartic operators. Through Monte Carlo simulations in the weak gauge-coupling limit, we show numerical evidence that the two-point vertex function of the gauge field in the mirror sector shows regular local behavior, and we argue that all you need is to kill the continuous mirror fermion symmetries with would-be gauge anomalies non-matched, as originally claimed by Eichten and Preskill. Finally, by gauging a U(1) subgroup of the U(1)$_A$$\times$ Spin(6)(SU(4)) of the previous model, we formulate the $2 1 (-1)^3$ chiral gauge model, and argue that the induced fermion measure term satisfies the required locality property and provides a solution to the reconstruction theorem formulated by Lüscher. This gives us “A New Hope” for the mission to be accomplished.

scholarly journals Coupling of a vector gauge field to a massive tensor field

2004 ◽  
Vol 596 (3-4) ◽  
pp. 301-305 ◽  
Author(s):  
S.V. Kuzmin ◽  
D.G.C. McKeon
Keyword(s):  
Gauge Field ◽  
Tensor Field ◽  
Vector Gauge
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