A Global Anomaly Threshold to Unsupervised Detection

2020 ◽  
pp. 119-149
Keyword(s):  
Global Anomaly

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.

Global Anomaly Detection Based on a Deep Prediction Neural Network

2019 ◽  
pp. 211-222
Author(s):  
Ang Li ◽  
Zhenjiang Miao ◽  
Yigang Cen ◽  
Vladimir Mladenovic ◽  
Liequan Liang ◽  
...  
Keyword(s):  
Neural Network ◽  
Anomaly Detection ◽  
Global Anomaly

Topological aspects of SU(2) Weyl fermion and global anomaly

1994 ◽  
Vol 35 (6) ◽  
pp. 2818-2827 ◽  
Author(s):  
Ashim Roy ◽  
Pratul Bandyopadhyay
Keyword(s):  
Global Anomaly ◽  
Weyl Fermion

scholarly journals A global anomaly from the Z-string

1997 ◽  
Vol 495 (1-2) ◽  
pp. 172-194 ◽  
Author(s):  
F.R. Klinkhamer ◽  
C. Rupp
Keyword(s):  
Global Anomaly

scholarly journals Vigorous deep-sea currents cause global anomaly in sediment accumulation in the Southern Ocean

Geology ◽  
2016 ◽  
Vol 44 (8) ◽  
pp. 663-666 ◽  
Author(s):  
Adriana Dutkiewicz ◽  
R. Dietmar Müller ◽  
Andrew McC. Hogg ◽  
Paul Spence
Keyword(s):  
Southern Ocean ◽  
Deep Sea ◽  
Sediment Accumulation ◽  
Sea Currents ◽  
Global Anomaly

scholarly journals AN O(3) GLOBAL ANOMALY IN 0+1 DIMENSION

1994 ◽  
Vol 09 (07) ◽  
pp. 623-630
Author(s):  
MINOS AXENIDES ◽  
HOLGER BECH NIELSEN ◽  
ANDREI JOHANSEN
Keyword(s):  
External Field ◽  
Dirac Operator ◽  
Degrees Of Freedom ◽  
Eigenvalue Spectrum ◽  
Level Crossing ◽  
One Dimensional ◽  
Exactly Solvable ◽  
Solvable Quantum ◽  
Global Anomaly ◽  
The One

We present a simple exactly solvable quantum mechanical example of the global anomaly in an O(3) model with an odd number of fermionic triplets coupled to a gauge field on a circle. Because the fundamental group is non-trivial, π1(O(3))=Z2, fermionic level crossing—circling occurs in the eigenvalue spectrum of the one-dimensional Dirac operator under continuous external field transformations. They are shown to be related to the presence of an odd number of normalizable zero modes in the spectrum of an appropriate two-dimensional Dirac operator. We argue that fermionic degrees of freedom in the presence of an infinitely large external field violate perturbative decoupling.

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.

GLOBAL ANOMALY MATCHING IN SUPERSYMMETRIC GAUGE THEORIES

1999 ◽  
Vol 14 (30) ◽  
pp. 2073-2082
Author(s):  
SIYE WU
Keyword(s):  
Gauge Theories ◽  
Matching Condition ◽  
Low Energy ◽  
Supersymmetric Gauge Theories ◽  
Gauge Invariant ◽  
Supersymmetric Gauge ◽  
Global Anomaly

We study the global anomaly matching condition in N=1 supersymmetric gauge theories. The condition provides an extra test, apart from the 't Hooft anomaly matching condition, to the validity of low energy descriptions in terms of gauge invariant composites or electric–magnetic duality.

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