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.

scholarly journals Topological terms and anomaly matching in effective field theories on ℝ3 × 𝕊1. Part I. Abelian symmetries and intermediate scales

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Erich Poppitz ◽  
F. David Wandler
Keyword(s):  
Effective Field Theories ◽  
Gauge Theories ◽  
Background Field ◽  
Effective Field ◽  
Field Theories ◽  
Global Symmetry ◽  
Dirac Fermions ◽  
Yang Mills ◽  
Local Background ◽  
Weyl Fermion

Abstract We explicitly calculate the topological terms that arise in IR effective field theories for SU(N) gauge theories on ℝ3 × 𝕊1 by integrating out all but the lightest modes. We then show how these terms match all global-symmetry ’t Hooft anomalies of the UV description. We limit our discussion to theories with abelian 0-form symmetries, namely those with one flavour of adjoint Weyl fermion and one or zero flavours of Dirac fermions. While anomaly matching holds as required, it takes a different form than previously thought. For example, cubic- and mixed-U(1) anomalies are matched by local background-field-dependent topological terms (background TQFTs) instead of chirallagrangian Wess-Zumino terms. We also describe the coupling of 0-form and 1-form symmetry backgrounds in the magnetic dual of super-Yang-Mills theory in a novel way, valid throughout the RG flow and consistent with the monopole-instanton ’t Hooft vertices. We use it to discuss the matching of the mixed chiral-center anomaly in the magnetic dual.

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.

scholarly journals ANTI-DE SITTER SPACE, THERMAL PHASE TRANSITION AND CONFINEMENT IN GAUGE THEORIES

2001 ◽  
Vol 16 (16) ◽  
pp. 2747-2769 ◽  
Author(s):  
EDWARD WITTEN
Keyword(s):  
Gauge Theories ◽  
De Sitter Space ◽  
Spontaneous Breaking ◽  
De Sitter ◽  
Four Dimensions ◽  
Yang Mills ◽  
Conformal Field ◽  
Classical Geometry ◽  
Large N ◽  
Quantum Phenomena

The correspondence between supergravity (and string theory) on AdS space and boundary conformal field theory relates the thermodynamics of [Formula: see text] super-Yang–Mills theory in four dimensions to the thermodynamics of Schwarzschild black holes in anti-de Sitter space. In this description, quantum phenomena such as the spontaneous breaking of the center of the gauge group, magnetic confinement and the mass gap are coded in classical geometry. The correspondence makes it manifest that the entropy of a very large AdS Schwarzschild black hole must scale "holographically" with the volume of its horizon. By similar methods, one can also make a speculative proposal for the description of large N gauge theories in four dimensions without supersymmetry.

scholarly journals Sp(4) gauge theories and beyond the standard model physics

2022 ◽  
Vol 258 ◽  
pp. 08003
Author(s):  
Biagio Lucini ◽  
Ed Bennett ◽  
Jack Holligan ◽  
Deog Ki Hong ◽  
Ho Hsiao ◽  
...  
Keyword(s):  
Gauge Theories ◽  
Beyond The Standard Model ◽  
Dirac Fermions ◽  
Gauge Model ◽  
Meson Spectrum ◽  
Main Motivation ◽  
Preliminary Results ◽  
The Standard Model ◽  
Glueball Spectrum ◽  
Antisymmetric Representation

We review numerical results for models with gauge group Sp(2N), discussing the glueball spectrum in the large-N limit, the quenched meson spectrum of Sp(4) with Dirac fermions in the fundamental and in the antisymmetric representation and the Sp(4) gauge model with two dynamical Dirac flavours. We also present preliminary results for the meson spectrum in the Sp(4) gauge theory with two fundamental and three antisymmetric Dirac flavours. The main motivation of our programme is to test whether this latter model is viable as a realisation of Higgs compositeness via the pseudo Nambu Goldstone mechanism and at the same time can provide partial top compositeness. In this respect, we report and briefly discuss preliminary results for the mass of the composite baryon made with two fundamental and one antisymmetric fermion (chimera baryon), whose physical properties are highly constrained if partial top compositeness is at work. Our investigation shows that a fully non-perturbative study of Higgs compositeness and partial top compositeness in Sp(4) is within reach with our current lattice methodology.

scholarly journals Composite and Background Fields in Non-Abelian Gauge Models

Symmetry ◽  
2020 ◽  
Vol 12 (12) ◽  
pp. 1985
Author(s):  
Pavel Yu. Moshin ◽  
Alexander A. Reshetnyak
Keyword(s):  
Effective Action ◽  
Green's Functions ◽  
Gauge Theories ◽  
Green’S Functions ◽  
Abelian Gauge ◽  
Systematic Analysis ◽  
Generating Functional ◽  
Yang Mills ◽  
Gauge Dependence ◽  
Background Fields

A joint introduction of composite and background fields into non-Abelian quantum gauge theories is suggested based on the symmetries of the generating functional of Green’s functions, with the systematic analysis focused on quantum Yang–Mills theories, including the properties of the generating functional of vertex Green’s functions (effective action). For the effective action in such theories, gauge dependence is found in terms of a nilpotent operator with composite and background fields, and on-shell independence from gauge fixing is established. The basic concept of a joint introduction of composite and background fields into non-Abelian gauge theories is extended to the Volovich–Katanaev model of two-dimensional gravity with dynamical torsion, as well as to the Gribov–Zwanziger theory.

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 Gauge Invariance and Mass Gap in (2+1)-Dimensional Yang–Mills Theory

1997 ◽  
Vol 12 (06) ◽  
pp. 1161-1171 ◽  
Author(s):  
Dimitra Karabali ◽  
V. P. Nair
Keyword(s):  
Gauge Invariance ◽  
Gauge Theories ◽  
Abelian Gauge ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Mass Gap ◽  
Spatial Dimensions

In terms of a gauge-invariant matrix parametrization of the fields, we give an analysis of how the mass gap could arise in non-Abelian gauge theories in two spatial dimensions.

scholarly journals NON-ABELIAN GAUGE THEORIES AS A CONSEQUENCE OF PERTURBATIVE QUANTUM GAUGE INVARIANCE

1999 ◽  
Vol 14 (21) ◽  
pp. 3421-3432 ◽  
Author(s):  
A. ASTE ◽  
G. SCHARF
Keyword(s):  
Gauge Theory ◽  
Gauge Invariance ◽  
Gauge Theories ◽  
Fundamental Concept ◽  
Abelian Gauge ◽  
Abelian Gauge Theory ◽  
Yang Mills ◽  
Vector Bosons ◽  
Perturbative Quantum

We show for the case of interacting massless vector bosons, how the structure of Yang–Mills theories emerges automatically from a more fundamental concept, namely perturbative quantum gauge invariance. It turns out that the coupling in a non-Abelian gauge theory is necessarily of Yang–Mills type plus divergence- and coboundary-couplings. The extension of the method to massive gauge theories is briefly discussed.

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