scholarly journals PANDORA'S BOX AND NON-SELFDUAL TOPOLOGICAL EXCITATIONS

2010 ◽  
Vol 25 (02n03) ◽  
pp. 278-288 ◽  
Author(s):  
MITHAT ÜNSAL
Keyword(s):  
Gauge Theories ◽  
Chiral Symmetry Breaking ◽  
Abelian Gauge ◽  
Topological Excitations ◽  
First Order ◽  
New Class ◽  
Self Duality ◽  
Large N ◽  
Composite Nature ◽  
Physical Phenomena

In the last few years, we have realized the existence of a new class of topological excitations, which are rather distinct from the platonic world of monopoles, monopole-instantons and instantons. All of the latter arise as solutions of the Prasad-Sommerfield type first order differential (self-duality) equations and have been extensively discussed in the context of confinement and chiral symmetry breaking for the last 30 years. However, new calculable deformations of asymptotically free chiral and vector-like gauge theories give us a new picture of these physical phenomena. Most often, the excitations which lead to confinement are not solutions to PS-type equations, they are non-selfdual and they are often bizarre. They are referred to as magnetic bions, triplets, and quintets, due to their composite nature. Bizarre as they are, combined with large-N volume independence, these novel non-self-dual excitations may also provide hope that at least some non-abelian gauge theories may be solvable.

scholarly journals Non-perturbative aspects of Sp(2N) gauge theories

2021 ◽  
Author(s):  
◽  
Jack Holligan
Keyword(s):  
Gauge Theories ◽  
Fine Tuning ◽  
Global Symmetry ◽  
Dirac Fermions ◽  
Open Problems ◽  
Abelian Gauge ◽  
General Behaviour ◽  
Yang Mills ◽  
Large N ◽  
Glueball Spectrum

Yang-Mills theories based on the symplectic groups – denoted by Sp(2N) – are inter-esting for both theoretical and phenomenological reasons. Sp(2N) theories with two fundamental Dirac fermions give rise to pseudo-Nambu-Goldstone bosons which can be interpreted as a composite Higgs particle. This framework can describe the existing Higgs boson without the need for unnatural fine-tuning. This justifies a programme of wider investigations of Sp(2N) gauge theories aimed at understanding their general behaviour. In this work, we study the glueball mass spectrum for Sp(2N) Yang-Mills theories using the variational method applied to Monte-Carlo generated gauge config-urations. This is carried out both for finite N and in the limit N → ∞. The results are compared to existing results for SU(N) Yang-Mills theories, again, for finite- and large-N. Our glueball analysis is then used to investigate some conjectures related to the behaviour of the spectrum in Yang-Mills theories based on a generic non-Abeliangauge group G. We also find numerical evidence that Sp(2N) groups confine both for finite and large N. As well as studying the glueball spectrum, we examine the quenched-meson spectrum for fermions in the fundamental, antisymmetric and sym-metric representations for N = 2 and N = 3. This study enables us to provide a first account of how the related observables vary with N. The investigations presented in this work contribute to our understanding of the non-perturbative dynamics of Sp(2N) gauge theories in connection with Higgs compositeness and, more in general, with fun-damental open problems in non-Abelian gauge theories such as confinement and global symmetry breaking.

scholarly journals Topological aspects of 4D Abelian lattice gauge theories with the θ parameter

2020 ◽  
Vol 2020 (12) ◽  
Author(s):  
Masazumi Honda ◽  
Yuya Tanizaki
Keyword(s):  
Phase Diagram ◽  
Gauge Theories ◽  
Global Symmetry ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Self Duality ◽  
Lattice Gauge ◽  
Lattice Gauge Theories ◽  
The Rich ◽  
Abelian Lattice

Abstract We study a four-dimensional U(1) gauge theory with the θ angle, which was originally proposed by Cardy and Rabinovici. It is known that the model has the rich phase diagram thanks to the presence of both electrically and magnetically charged particles. We discuss the topological nature of the oblique confinement phase of the model at θ = π, and show how its appearance can be consistent with the anomaly constraint. We also construct the SL(2, ℤ) self-dual theory out of the Cardy-Rabinovici model by gauging a part of its one-form symmetry. This self-duality has a mixed ’t Hooft anomaly with gravity, and its implications on the phase diagram is uncovered. As the model shares the same global symmetry and ’t Hooft anomaly with those of SU(N) Yang-Mills theory, studying its topological aspects would provide us more hints to explore possible dynamics of non-Abelian gauge theories with nonzero θ angles.

TORONS, CHIRAL SYMMETRY BREAKING AND U(1) PROBLEM IN QCD AND SQCD

1989 ◽  
Vol 04 (23) ◽  
pp. 2251-2258 ◽  
Author(s):  
A.R. ZHITNITSKY
Keyword(s):  
Symmetry Breaking ◽  
Chiral Symmetry ◽  
Crucial Role ◽  
Topological Charge ◽  
Gauge Theories ◽  
Chiral Symmetry Breaking ◽  
Dual Solutions ◽  
New Class ◽  
Manifold With Boundary ◽  
The Continuum

The new class of self-dual solutions with fractional topological charge in SU(2) gauge theories is considered. The solution is defined on manifold with boundary, it has topological charge Q=1/2 and action S=(8π2)/g2×Q. The contribution of the corresponding fluctuations to chiral condensates [Formula: see text], <λ2> in SQCD is calculated and it is consistent with Konishi anomaly. For the fermion condensate in QCD (with Nf=Nc=2, m→0) we find [Formula: see text], [Formula: see text]. The unbound resonances of the continuum at λ=0 play a crucial role in this calculation.

scholarly journals Solitary Waves in Abelian Gauge Theories

2008 ◽  
Vol 8 (2) ◽  
Author(s):  
Vieri Benci ◽  
Donato Fortunato
Keyword(s):  
Electromagnetic Field ◽  
Electromagnetic Fields ◽  
Solitary Waves ◽  
Lower Order ◽  
Gauge Theories ◽  
Order Term ◽  
Lower Order Term ◽  
Field Equations ◽  
Abelian Gauge ◽  
Physical Phenomena

AbstractAbelian gauge theories consist of a class of field equations which provide a model for the interaction between matter and electromagnetic fields. In this paper we analyze the existence of solitary waves for these theories. We assume that the lower order term W is positive and we prove the existence of solitary waves if the coupling between matter and electromagnetic field is small. We point out that the positiveness assumption on W implies that the energy is positive: this fact makes these theories more suitable to model physical phenomena.

Duality and large N limit in non-abelian gauge theories

1984 ◽  
Vol 139 (5-6) ◽  
pp. 374-378 ◽  
Author(s):  
Leah Mizrachi
Keyword(s):  
Gauge Theories ◽  
Abelian Gauge ◽  
Large N

scholarly journals ON THE EQUIVALENCE BETWEEN TOPOLOGICALLY AND NON-TOPOLOGICALLY MASSIVE ABELIAN GAUGE THEORIES

2000 ◽  
Vol 15 (02) ◽  
pp. 121-131 ◽  
Author(s):  
E. HARIKUMAR ◽  
M. SIVAKUMAR
Keyword(s):  
Correlation Function ◽  
Gauge Theory ◽  
Phase Space ◽  
Gauge Theories ◽  
Abelian Gauge ◽  
First Order ◽  
Space Extension ◽  
Canonical Variables ◽  
Canonical Approach ◽  
Total Divergence

We analyze the equivalence between topologically massive gauge theory (TMGT) and different formulations of non-topologically massive gauge theories (NTMGTs) in the canonical approach. The different NTMGTs studied are Stückelberg formulation of (a) a first-order formulation involving one- and two-form fields, (b) Proca theory, and (c) massive Kalb–Ramond theory. We first quantize these reducible gauge systems by using the phase space extension procedure and using it, identify the phase space variables of NTMGTs which are equivalent to the canonical variables of TMGT and show that under this the Hamiltonian also get mapped. Interestingly it is found that the different NTMGTs are equivalent to different formulations of TMGTs which differ only by a total divergence term. We also provide covariant mappings between the fields in TMGT to NTMGTs at the level of correlation function.

Geometry and Quantum Dynamics

2017 ◽  
Author(s):  
Laurent Baulieu ◽  
John Iliopoulos ◽  
Roland Sénéor
Keyword(s):  
General Relativity ◽  
Quantum Dynamics ◽  
Gauge Theories ◽  
Brst Symmetry ◽  
Abelian Gauge ◽  
Yang Mills ◽  
History Of ◽  
Brst Invariance

A geometrical derivation of Abelian and non- Abelian gauge theories. The Faddeev–Popov quantisation. BRST invariance and ghost fields. General discussion of BRST symmetry. Application to Yang–Mills theories and general relativity. A brief history of gauge theories.

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