Global gauge anomaly and James numbers of Stiefel manifolds

1988 ◽  
Vol 38 (6) ◽  
pp. 1880-1887 ◽  
Author(s):  
Huazhong Zhang ◽  
Susumu Okubo
Keyword(s):  
Stiefel Manifolds ◽  
Global Gauge ◽  
Gauge Anomaly

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

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.

scholarly journals Zero-Dimensional Analogue of the Global Gauge Anomaly

2006 ◽  
Vol 115 (2) ◽  
pp. 467-471
Author(s):  
H. So ◽  
H. Suzuki
Keyword(s):  
Global Gauge ◽  
Gauge Anomaly

scholarly journals Z-string global gauge anomaly and Lorentz non-invariance

1998 ◽  
Vol 535 (1-2) ◽  
pp. 233-241 ◽  
Author(s):  
F.R. Klinkhamer
Keyword(s):  
Global Gauge ◽  
Gauge Anomaly

Invariant Einstein metrics on $\mathrm{SU}(n)$ and complex Stiefel manifolds

2020 ◽  
Vol 72 (2) ◽  
pp. 161-210 ◽  
Author(s):  
Andreas Arvanitoyeorgos ◽  
Yusuke Sakane ◽  
Marina Statha
Keyword(s):  
Einstein Metrics ◽  
Stiefel Manifolds

Discrete Geodesic Flows on Stiefel Manifolds

2020 ◽  
Vol 310 (1) ◽  
pp. 163-174
Author(s):  
Božidar Jovanović ◽  
Yuri N. Fedorov
Keyword(s):  
Geodesic Flows ◽  
Stiefel Manifolds

scholarly journals Whitehead products in the complex Stiefel manifolds

1983 ◽  
Vol 26 (2) ◽  
pp. 241-251 ◽  
Author(s):  
Yasukuni Furukawa
Keyword(s):  
Stiefel Manifold ◽  
Isotropy Group ◽  
Homotopy Groups ◽  
Stiefel Manifolds

The complex Stiefel manifoldWn,k, wheren≦k≦1, is a space whose points arek-frames inCn. By using the formula of McCarty [4], we will make the calculations of the Whitehead products in the groups π*(Wn,k). The case of real and quaternionic will be treated by Nomura and Furukawa [7]. The product [[η],j1l] appears as generator of the isotropy group of the identity map of Stiefel manifolds. In this note we use freely the results of the 2-components of the homotopy groups of real and complex Stiefel manifolds such as Paechter [8], Hoo-Mahowald [1], Nomura [5], Sigrist [9] and Nomura-Furukawa [6].

scholarly journals Supersymmetric gauge anomaly with general homotopic paths

2001 ◽  
Vol 596 (1-2) ◽  
pp. 315-347 ◽  
Author(s):  
S.James Gates ◽  
Marcus T. Grisaru ◽  
Marcia E. Knutt ◽  
Silvia Penati ◽  
Hiroshi Suzuki
Keyword(s):  
Supersymmetric Gauge ◽  
Gauge Anomaly

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.

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