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 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 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 Real forms of extended Kac–Moody symmetries and higher spin gauge theories

2012 ◽  
Vol 44 (7) ◽  
pp. 1787-1834 ◽  
Author(s):  
Marc Henneaux ◽  
Axel Kleinschmidt ◽  
Hermann Nicolai
Keyword(s):  
Gauge Theories ◽  
Higher Spin ◽  
Real Forms

scholarly journals On     1, 2, 4 higher spin gauge theories in four dimensions

2002 ◽  
Vol 19 (23) ◽  
pp. 6175-6196 ◽  
Author(s):  
J Engquist ◽  
E Sezgin ◽  
P Sundell
Keyword(s):  
Gauge Theories ◽  
Four Dimensions ◽  
Higher Spin

ON THE QUANTIZATION OF A THEORY WITH GLOBAL GAUGE ANOMALIES

1987 ◽  
Vol 02 (12) ◽  
pp. 977-982 ◽  
Author(s):  
ROBERTO PERCACCI
Keyword(s):  
Gauge Theories ◽  
Global Gauge ◽  
Gauge Anomalies

It is shown that the Faddeev-Shatashvili approach to the quantization of anomalous gauge theories can be extended to the case of global gauge anomalies.

Sign in / Sign up

Export Citation Format

Share Document