scholarly journals Functorial QFT, Gauge Anomalies¶and the Dirac Determinant Bundle

2001 ◽  
Vol 219 (3) ◽  
pp. 567-605 ◽  
Author(s):  
Jouko Mickelsson ◽  
Simon Scott
Keyword(s):  
Determinant Bundle ◽  
Gauge Anomalies

scholarly journals BRST and Superfield Formalism—A Review

Universe ◽  
2021 ◽  
Vol 7 (8) ◽  
pp. 280
Author(s):  
Loriano Bonora ◽  
Rudra Prakash Malik
Keyword(s):  
Riemannian Geometry ◽  
Gauge Theories ◽  
Original Material ◽  
Comprehensive Description ◽  
Higher Spin ◽  
Gauge Anomalies

This article, which is a review with substantial original material, is meant to offer a comprehensive description of the superfield representations of BRST and anti-BRST algebras and their applications to some field-theoretic topics. After a review of the superfield formalism for gauge theories, we present the same formalism for gerbes and diffeomorphism invariant theories. The application to diffeomorphisms leads, in particular, to a horizontal Riemannian geometry in the superspace. We then illustrate the application to the description of consistent gauge anomalies and Wess–Zumino terms for which the formalism seems to be particularly tailor-made. The next subject covered is the higher spin YM-like theories and their anomalies. Finally, we show that the BRST superfield formalism applies as well to the N=1 super-YM theories formulated in the supersymmetric superspace, for the two formalisms go along with each other very well.

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 Electric dipole moments, new forces and dark matter

2021 ◽  
Vol 2021 (3) ◽  
Author(s):  
Pavel Fileviez Pérez ◽  
Alexis D. Plascencia
Keyword(s):  
Dark Matter ◽  
Electric Dipole ◽  
Dipole Moments ◽  
Dark Matter Candidate ◽  
Beyond The Standard Model ◽  
Electric Dipole Moments ◽  
Dark Matter Relic Density ◽  
New States ◽  
Gauge Anomalies ◽  
The Impact

Abstract New sources of CP violation beyond the Standard Model are crucial to explain the baryon asymmetry in the Universe. We discuss the impact of new CP violating interactions in theories where a dark matter candidate is predicted by the cancellation of gauge anomalies. In these theories, the constraint on the dark matter relic density implies an upper bound on the new symmetry breaking scale from which all new states acquire their masses. We investigate in detail the predictions for electric dipole moments and show that if the relevant CP-violating phase is large, experiments such as the ACME collaboration will be able to fully probe the theory.

scholarly journals Dimers, orientifolds and anomalies

2021 ◽  
Vol 2021 (2) ◽  
Author(s):  
Riccardo Argurio ◽  
Matteo Bertolini ◽  
Sebastián Franco ◽  
Eduardo García-Valdecasas ◽  
Shani Meynet ◽  
...  
Keyword(s):  
Physical Properties ◽  
Gauge Theories ◽  
Geometric Properties ◽  
Dimer Model ◽  
Gauge Anomalies

Abstract We study 4d$$ \mathcal{N} $$ N = 1 gauge theories engineered via D-branes at orientifolds of toric singularities, where gauge anomalies are cancelled without the introduction of non-compact flavor branes. Using dimer model techniques, we derive geometric criteria for establishing whether a given singularity can admit anomaly-free D-brane configurations purely based on its toric data and the type of orientifold projection. Our results therefore extend the dictionary between geometric properties of singularities and physical properties of the corresponding gauge theories.

scholarly journals Some comments on 6d global gauge anomalies

2021 ◽  
Author(s):  
Yasunori Lee ◽  
Yuji Tachikawa
Keyword(s):  
Point Of View ◽  
Homotopy Groups ◽  
Proper Treatment ◽  
Anomaly Cancellation ◽  
The Past ◽  
Global Gauge ◽  
Gauge Anomalies

Abstract Global gauge anomalies in 6d associated with non-trivial homotopy groups π6(G) for G = SU(2), SU(3), and G2 were computed and utilized in the past. In the modern bordism point of view of anomalies, however, they come from the bordism groups Ω7spin (BG), which are in fact trivial and therefore preclude their existence. Instead, it was noticed that a proper treatment of the 6d Green-Schwarz mechanism reproduces the same anomaly cancellation conditions derived from π6(G). In this paper, we revisit and clarify the relation between these two different approaches.

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