ON THE QUANTIZATION OF A THEORY WITH GLOBAL 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.

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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.

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Dimers, orientifolds and anomalies

Journal of High Energy Physics ◽

10.1007/jhep02(2021)153 ◽

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.

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Some comments on 6d global gauge anomalies

Progress of Theoretical and Experimental Physics ◽

10.1093/ptep/ptab015 ◽

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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NON-PERTURBAITVE GREEN FUNCTIONS IN QUANTUM GAUGE THEORIES

Modern Physics Letters A ◽

10.1142/s0217732391000956 ◽

1991 ◽

Vol 06 (10) ◽

pp. 909-921 ◽

Cited By ~ 6

Author(s):

S.V. SHABANOV

Keyword(s):

Configuration Space ◽

Gauge Theories ◽

Gauge Condition ◽

Green Functions ◽

Spatial Infinity ◽

Gauge Invariant ◽

Yang Mills ◽

Global Gauge

Non-perturbative Green functions for gauge invariant variables are considered. The Green functions are found to be modified as compared with the usual ones in a definite gauge because of a physical configuration space (PCS) reduction. In the Yang-Mills theory with fermions, this phenomenon follows from the Singer theorem about the absence of a global gauge condition for the fields tending to zero at spatial infinity.

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Topological orders with global gauge anomalies

Physical Review B ◽

10.1103/physrevb.92.054410 ◽

2015 ◽

Vol 92 (5) ◽

Cited By ~ 5

Author(s):

Yi-Zhuang You ◽

Cenke Xu

Keyword(s):

Global Gauge ◽

Gauge Anomalies

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SOME GLOBAL ASPECTS OF GAUGE ANOMALIES OF SEMISIMPLE GAUGE GROUPS AND FERMION GENERATIONS IN GUT AND SUPERSTRING THEORIES

International Journal of Modern Physics A ◽

10.1142/s0217751x06025341 ◽

2006 ◽

Vol 21 (05) ◽

pp. 1033-1052

Author(s):

HUAZHONG ZHANG

Keyword(s):

Gauge Group ◽

Complete Proof ◽

Gauge Groups ◽

Gauge Transformations ◽

Global Gauge ◽

Global Anomaly ◽

Gauge Anomalies ◽

Physical Consequences ◽

Gauge Anomaly ◽

Weyl Fermions

We study more extensively and completely for global gauge anomalies with some semisimple gauge groups as initiated in Ref. 1. A detailed and complete proof or derivation is provided for the Z2 global (nonperturbative) gauge anomaly given in Ref. 1 for a gauge theory with the semisimple gauge group SU (2) × SU (2) × SU (2) in D = 4 dimensions and Weyl fermions in the irreducible representation (IR) ω = (2, 2, 2) with 2 denoting the corresponding dimensions. This Z2 anomaly was used in the discussions related to all the generic SO (10) and supersymmetric SO (10) unification theories1 for the total generation numbers of fermions and mirror fermions. Our result1 shows that the global anomaly coefficient formula is given by A(ω) = exp [iπQ2(□)] = -1 in this case with Q2(□) being the Dynkin index for SU (8) in the fundamental IR (□) = (8) and that the corresponding gauge transformations need to be topologically nontrivial simultaneously in all the three SU (2) factors for the homotopy group Π4( SU (2) × SU (2) × SU (2))is also discussed, and as shown by the results1 the semisimple gauge transformations collectively may have physical consequences which do not correspond to successive simple gauge transformations. The similar result given in Ref. 1 for the Z2 global gauge anomaly of gauge group SU (2) × SU (2) with Weyl fermions in the IR ω = (2, 2) with 2 denoting the corresponding dimensions is also discussed with proof similar to the case of SU (2) × SU (2) × SU (2). We also give a complete proof for some relevant topological results. We expect that our results and discussions may also be useful in more general studies related to global aspects of gauge theories. Gauge anomalies for the relevant semisimple gauge groups are also briefly discussed in higher dimensions, especially for self-contragredient representations, with discussions involving trace identities relating to Ref. 15. We also relate the discussions to our results and propositions in our previous studies of global gauge anomalies. We also remark the connection of our results and discussions to the total generation numbers in relevant theories.

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