scholarly journals Gauge anomaly cancellation in chiral gauge theories

2012 ◽  
Vol 327 (6) ◽  
pp. 1435-1449 ◽  
Author(s):  
Gabriel Di Lemos Santiago Lima ◽  
Rafael Chaves ◽  
Sebastião Alves Dias
Keyword(s):  
Gauge Theories ◽  
Anomaly Cancellation ◽  
Gauge Anomaly

scholarly journals On Gauge Invariance of the Bosonic Measure in Chiral Gauge Theories

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 283
Author(s):  
Gabriel de Lima e Silva ◽  
Thalis José Girardi ◽  
Sebastião Alves Dias
Keyword(s):  
Hilbert Space ◽  
Gauge Theory ◽  
Path Integral ◽  
Gauge Invariance ◽  
Gauge Theories ◽  
Direct Calculation ◽  
Identity Operator ◽  
Anomaly Cancellation ◽  
Gauge Anomaly ◽  
General Gauge

Gauge invariance of the measure associated with the gauge field is usually taken for granted, in a general gauge theory. We furnish a proof of this invariance, within Fujikawa’s approach. To stress the importance of this fact, we briefly review gauge anomaly cancellation as a consequence of gauge invariance of the bosonic measure and compare this cancellation to usual results from algebraic renormalization, showing that there are no potential inconsistencies. Then, using a path integral argument, we show that a possible Jacobian for the gauge transformation has to be the identity operator, in the physical Hilbert space. We extend the argument to the complete Hilbert space by a direct calculation.

COMMENTS ON ORIENTIFOLD OF BRANE TILINGS

2008 ◽  
Vol 23 (14n15) ◽  
pp. 2299-2306
Author(s):  
YOSUKE IMAMURA ◽  
KEISUKE KIMURA ◽  
MASAHITO YAMAZAKI
Keyword(s):  
Conservation Law ◽  
Gauge Theories ◽  
Anomaly Cancellation ◽  
Charge Conservation ◽  
Gauge Anomaly

The relation between brane charge conservation law in fivebrane system described by orientifolded brane tilings and the gauge anomaly cancellation in the corresponding gauge theories is summarized.

scholarly journals A note on gauge anomaly cancellation in effective field theories

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Ferruccio Feruglio
Keyword(s):  
Effective Field Theories ◽  
Effective Field ◽  
Field Theories ◽  
Anomaly Cancellation ◽  
Charge Assignment ◽  
The Standard Model ◽  
Renormalizable Theory ◽  
Complete Set ◽  
Gauge Anomalies ◽  
Gauge Anomaly

Abstract The conditions for the absence of gauge anomalies in effective field theories (EFT) are rivisited. General results from the cohomology of the BRST operator do not prevent potential anomalies arising from the non-renormalizable sector, when the gauge group is not semi-simple, like in the Standard Model EFT (SMEFT). By considering a simple explicit model that mimics the SMEFT properties, we compute the anomaly in the regularized theory, including a complete set of dimension six operators. We show that the dependence of the anomaly on the non-renormalizable part can be removed by adding a local counterterm to the theory. As a result the condition for gauge anomaly cancellation is completely controlled by the charge assignment of the fermion sector, as in the renormalizable theory.

scholarly journals Omega vs. pi, and 6d anomaly cancellation

2021 ◽  
Vol 2021 (5) ◽  
Author(s):  
Joe Davighi ◽  
Nakarin Lohitsiri
Keyword(s):  
Gauge Theories ◽  
Necessary Conditions ◽  
Homotopy Groups ◽  
Mapping Torus ◽  
Anomaly Cancellation ◽  
Global Anomaly ◽  
Gauge Anomalies ◽  
Local Anomalies ◽  
Dimensional Mapping

Abstract In this note we review the role of homotopy groups in determining non-perturbative (henceforth ‘global’) gauge anomalies, in light of recent progress understanding global anomalies using bordism. We explain why non-vanishing of πd(G) is neither a necessary nor a sufficient condition for there being a possible global anomaly in a d-dimensional chiral gauge theory with gauge group G. To showcase the failure of sufficiency, we revisit ‘global anomalies’ that have been previously studied in 6d gauge theories with G = SU(2), SU(3), or G2. Even though π6(G) ≠ 0, the bordism groups $$ {\Omega}_7^{\mathrm{Spin}}(BG) $$ Ω 7 Spin BG vanish in all three cases, implying there are no global anomalies. In the case of G = SU(2) we carefully scrutinize the role of homotopy, and explain why any 7-dimensional mapping torus must be trivial from the bordism perspective. In all these 6d examples, the conditions previously thought to be necessary for global anomaly cancellation are in fact necessary conditions for the local anomalies to vanish.

scholarly journals Anomaly cancellation in three-dimensional noncommutative gauge theories

2007 ◽  
Vol 656 (1-3) ◽  
pp. 145-151 ◽  
Author(s):  
M. Gomes ◽  
T. Mariz ◽  
J.R. Nascimento ◽  
A.Yu. Petrov ◽  
A.J. da Silva ◽  
...  
Keyword(s):  
Gauge Theories ◽  
Three Dimensional ◽  
Anomaly Cancellation ◽  
Noncommutative Gauge Theories

scholarly journals Analysis of an SU(8) model with a spin-1 2 field directly coupled to a gauged Rarita–Schwinger spin-3 2 field

2019 ◽  
Vol 34 (33) ◽  
pp. 1950230
Author(s):  
Stephen L. Adler
Keyword(s):  
Representation Formula ◽  
Root Lattice ◽  
Anomaly Cancellation ◽  
Text Field ◽  
Text Model ◽  
Gauge Anomaly ◽  
Chiral Representation

In earlier work we analyzed an abelianized model in which a gauged Rarita–Schwinger spin-[Formula: see text] field is directly coupled to a spin-[Formula: see text] field. Here, we extend this analysis to the gauged [Formula: see text] model for which the abelianized model was a simplified substitute. We calculate the gauge anomaly, show that anomaly cancellation requires adding an additional left chiral representation [Formula: see text] spin-[Formula: see text] fermion to the original fermion complement of the [Formula: see text] model, and give options for restoring boson–fermion balance. We conclude with a summary of attractive features of the reformulated [Formula: see text] model, including a possible connection to the [Formula: see text] root lattice.

scholarly journals Anomaly cancellation and conformality in quiver gauge theories

2006 ◽  
Vol 638 (4) ◽  
pp. 374-381 ◽  
Author(s):  
Edoardo Di Napoli ◽  
Paul H. Frampton
Keyword(s):  
Gauge Theories ◽  
Anomaly Cancellation

Ward–Takahashi identities for Abelian chiral gauge theories

2016 ◽  
Vol 31 (11) ◽  
pp. 1650062
Author(s):  
Ana Paula Cardoso Rodrigues de Lima ◽  
Sebastião Alves Dias
Keyword(s):  
Gauge Theory ◽  
Future Study ◽  
Gauge Theories ◽  
Charge Renormalization ◽  
Renormalization Constants ◽  
Gauge Anomaly

By considering a general Abelian chiral gauge theory, we investigate the behavior of anomalous Ward–Takahashi (WT) identities concerning their prediction for the usual relationship between the vertex and two-point fermion functions. Using gauge anomaly vanishing results, we show that the usual (in the nonanomalous case) WT identity connecting the vertex and two-point fermion 1PI functions is modified for Abelian chiral gauge theories. The modification, however, implies a relation between fermion and charge renormalization constants that can be important in a future study of renormalization of such theories.

scholarly journals One-loop perturbative coupling of A and A★ through the chiral overlap operator

2018 ◽  
Vol 175 ◽  
pp. 11013
Author(s):  
Hiroki Makino ◽  
Okuto Morikawa ◽  
Hiroshi Suzuki
Keyword(s):  
Gauge Field ◽  
Effective Action ◽  
Gauge Theories ◽  
Gradient Flow ◽  
Tree Level ◽  
Anomaly Cancellation ◽  
Interaction Terms ◽  
Left Handed ◽  
The Right ◽  
The Continuum

Recently, Grabowska and Kaplan constructed a four-dimensional lattice formulation of chiral gauge theories on the basis of the chiral overlap operator. At least in the tree-level approximation, the left-handed fermion is coupled only to the original gauge field A, while the right-handed one is coupled only to the gauge field A*, a deformation of A by the gradient flow with infinite flow time. In this paper, we study the fermion one-loop effective action in their formulation. We show that the continuum limit of this effective action contains local interaction terms between A and A*, even if the anomaly cancellation condition is met. These non-vanishing terms would lead an undesired perturbative spectrum in the formulation.

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