scholarly journals The global gauge group structure of F-theory compactification with U(1)s

2018 ◽  
Vol 2018 (1) ◽  
Author(s):  
Mirjam Cvetič ◽  
Ling Lin
Keyword(s):  
Gauge Group ◽  
Group Structure ◽  
Global Gauge

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 On the underlying gauge group structure of D=11 supergravity

2004 ◽  
Vol 596 (1-2) ◽  
pp. 145-155 ◽  
Author(s):  
I.A. Bandos ◽  
J.A. de Azcárraga ◽  
J.M. Izquierdo ◽  
M. Picón ◽  
O. Varela
Keyword(s):  
Gauge Group ◽  
Group Structure

scholarly journals A STUDY OF THE INFLUENCE OF THE GAUGE GROUP ON THE DYSON–SCHWINGER EQUATIONS FOR SCALAR-YANG–MILLS SYSTEMS

2012 ◽  
Vol 27 (18) ◽  
pp. 1250098 ◽  
Author(s):  
VERONIKA MACHER ◽  
AXEL MAAS ◽  
REINHARD ALKOFER
Keyword(s):  
Numerical Simulations ◽  
Gauge Group ◽  
Correlation Functions ◽  
Group Structure ◽  
Qualitative Behavior ◽  
Yang Mills ◽  
Structural Differences ◽  
Matter Fields ◽  
Insight Into

The particular choice of the gauge group for Yang–Mills theory plays an important role when it comes to the influence of matter fields. In particular, both the chosen gauge group and the representation of the matter fields yield structural differences in the quenched case. Especially, the qualitative behavior of the Wilson potential is strongly dependent on this selection. Though the algebraic reasons for this observation is clear, it is far from obvious how this behavior can be described besides using numerical simulations. Herein, it is investigated how the group structure appears in the Dyson–Schwinger equations, which as a hierarchy of equations for the correlation functions have to be satisfied. It is found that there are differences depending on both the gauge group and the representation of the matter fields. This provides insight into possible truncation schemes for practical calculations using these equations.

scholarly journals On the gauge symmetries of the spinning particle

2014 ◽  
Vol 92 (5) ◽  
pp. 411-414
Author(s):  
N. Kiriushcheva ◽  
S.V. Kuzmin ◽  
D.G.C. McKeon
Keyword(s):  
Simple Model ◽  
Gauge Group ◽  
Gauge Transformation ◽  
Group Structure ◽  
Simple Algebra ◽  
Direct Examination ◽  
Spinning Particle ◽  
Gauge Transformations ◽  
Gauge Symmetries ◽  
New Variables

We reconsider the gauge symmetries of the spinning particle by a direct examination of the Lagrangian using a systematic procedure based on the Noether identities. It proves possible to find a set of local bosonic and fermionic gauge transformations that have a simple gauge group structure, which is a true Lie algebra, both for the massless and massive case. This new fermionic gauge transformation of the “position” and “spin” variables in the action decouples from that of the “einbein” and “gravitino”. It is also possible to redefine the fields so that this simple algebra of commutators of the gauge transformations can be derived directly starting from the Lagrangian written in these new variables. We discuss a possible extension of our analysis of this simple model to more complicated cases.

scholarly journals The Lie group of vertical bisections of a regular Lie groupoid

2020 ◽  
Vol 32 (2) ◽  
pp. 479-489
Author(s):  
Alexander Schmeding
Keyword(s):  
Lie Groups ◽  
Gauge Group ◽  
Lie Group ◽  
Group Structure ◽  
Lie Groupoids ◽  
Gauge Groups ◽  
Infinite Dimensional ◽  
Lie Groupoid ◽  
Regularity Properties ◽  
Infinite Dimensional Lie Group

AbstractIn this note we construct an infinite-dimensional Lie group structure on the group of vertical bisections of a regular Lie groupoid. We then identify the Lie algebra of this group and discuss regularity properties (in the sense of Milnor) for these Lie groups. If the groupoid is locally trivial, i.e., a gauge groupoid, the vertical bisections coincide with the gauge group of the underlying bundle. Hence, the construction recovers the well-known Lie group structure of the gauge groups. To establish the Lie theoretic properties of the vertical bisections of a Lie groupoid over a non-compact base, we need to generalise the Lie theoretic treatment of Lie groups of bisections for Lie groupoids over non-compact bases.

Some effects of unequal distribution of information in a wheel group structure.

1954 ◽  
Vol 49 (4, Pt.1) ◽  
pp. 554-556 ◽  
Author(s):  
J. C. Gilchrist ◽  
Marvin E. Shaw ◽  
L. C. Walker
Keyword(s):  
Group Structure ◽  
Unequal Distribution
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