Anomaly cancellation condition in an effective nonperturbative electroweak theory

AbstractWe establish the Thom isomorphism in twisted K-theory for any real vector bundle and develop the push-forward map in twisted K-theory for any differentiable map f : X → Y (not necessarily K-oriented). We also obtain the wrong way functoriality property for the push-forward map in twisted K-theory. For D-branes satisfying Freed-Witten's anomaly cancellation condition in a manifold with a non-trivial B-field, we associate a canonical element in the twisted K-group to get the so-called D-brane charges.

Download Full-text

GAUGED WZW MODELS VIA EQUIVARIANT COHOMOLOGY

Modern Physics Letters A ◽

10.1142/s0217732311035754 ◽

2011 ◽

Vol 26 (18) ◽

pp. 1343-1352

Author(s):

HUGO GARCÍA-COMPEÁN ◽

PABLO PANIAGUA

Keyword(s):

Equivariant Cohomology ◽

Higher Dimensions ◽

Dimensional Case ◽

Two Dimensional ◽

Anomaly Cancellation ◽

Gauge Invariant ◽

Cancellation Condition ◽

Four Dimensions ◽

Invariant Extension

The problem of finding a systematic computation of the gauge-invariant extension of WZW term by using equivariant cohomology is addressed. Witten's analysis for the two-dimensional case is extended to higher dimensions, in particular to four dimensions. It is shown that Cartan's model is used to find the anomaly cancellation condition while Weil's model is more appropriated to express the gauge-invariant extension of the WZW term. In the process we point out that both models are also useful to emphasize some nice relations with the Abelian anomaly.

Download Full-text

About electrodynamics, standard model and the quantization of the electrical charge

International Journal of Modern Physics A ◽

10.1142/s0217751x18502056 ◽

2018 ◽

Vol 33 (33) ◽

pp. 1850205

Author(s):

Renata Jora

Keyword(s):

Partition Function ◽

Standard Model ◽

Gauge Field ◽

Consistency Condition ◽

Field Method ◽

Electrical Charge ◽

Ward Identities ◽

Anomaly Cancellation ◽

Cancellation Condition ◽

The Standard Model

The quantization of the electrical charge in the electrodynamics and of the hypercharge in the standard model are imposed in the theory based not on theoretical arguments but on the experimental observations. In this paper we propose a quantum consistency condition in a theory where Ward identities are respected that requires the quantization of the charge within the framework of the theory without external impositions. This refers to the renormalization conditions in the background gauge field method such that to ensure a correct mathematical correspondence between the bare partition function and the renormalized one. Applied to the standard model of elementary particles our criterion together with the anomaly cancellation condition leads to the correct hypercharge assignment of all standard model fermions.

Download Full-text

H → γγ, gauge invariance, and the hierarchy problem

International Journal of Modern Physics A ◽

10.1142/s0217751x16300465 ◽

2016 ◽

Vol 31 (26) ◽

pp. 1630046 ◽

Cited By ~ 2

Author(s):

Jennifer Kile

Keyword(s):

Gauge Invariance ◽

Dimensional Regularization ◽

Hierarchy Problem ◽

Anomaly Cancellation ◽

Gauge Invariant ◽

Loop Contribution ◽

Cancellation Condition ◽

Interesting Possibility ◽

Interesting Behavior ◽

Finite Result

The calculation of [Formula: see text] displays interesting behavior which depends on the regulator used in the integration over loop momenta. If calculated using a gauge-invariant regulator, such as dimensional regularization, the calculation yields a unique, finite, gauge-invariant result. If four-dimensional symmetric regulation is used without finite subtractions, additional pieces occur which spoil QED gauge invariance. In both cases, a finite result is obtained, but the particular finite result depends on the regulator utilized in the calculation. While gauge-invariant regulators such as dimensional regularization are normally used, four-dimensional symmetric integration is also physically motivated. Also, the gauge-invariance-violating terms that arise using four-dimensional symmetric integration are of the same form for the fermionic, scalar, and the SM [Formula: see text] loop calculated in renormalizable gauge. This presents an interesting possibility. Inspired by anomaly cancellation, we ask if it is possible that these gauge-invariance-violating terms may cancel in certain models when contributions from all diagrams are included. Here, we calculate the regulator-dependent contributions to [Formula: see text] arising from generic fermion and scalar loops, as well as the Standard Model [Formula: see text] loop contribution, which we evaluate in renormalizable gauge for general [Formula: see text]. We find that a cancellation between such terms is possible, and derive the cancellation condition. Additionally, we find that this cancellation condition ensures QED gauge invariance without finite subtractions for any regulator used, not just for four-dimensional symmetric integration. We additionally relate the regulator-dependent terms in [Formula: see text] to the behavior of quadratically-divergent Higgs tadpole diagrams under shifts of internal loop momentum. Thus, the cancellation condition for the gauge-invariance-violating terms in [Formula: see text] implies a relation between the quadratic divergences in Higgs tadpole diagrams; this has consequences for hypothesized solutions to the hierarchy problem. Lastly, we find that the MSSM obeys our cancellation condition.

Download Full-text

A note on gauge anomaly cancellation in effective field theories

Journal of High Energy Physics ◽

10.1007/jhep03(2021)128 ◽

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.

Download Full-text

Anomaly cancellation in seven-dimensional supergravity with a boundary

Physical Review D ◽

10.1103/physrevd.68.065019 ◽

2003 ◽

Vol 68 (6) ◽

Cited By ~ 14

Author(s):

Tony Gherghetta ◽

Alex Kehagias

Keyword(s):

Anomaly Cancellation

Download Full-text

Omega vs. pi, and 6d anomaly cancellation

Journal of High Energy Physics ◽

10.1007/jhep05(2021)267 ◽

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.

Download Full-text