Emergent Yang–Mills theories from universal extra dimensions

2017 ◽  
Vol 32 (05) ◽  
pp. 1750029
Author(s):  
J. L. Chkareuli ◽  
Z. Kepuladze
Keyword(s):  
Vector Field ◽  
Scalar Field ◽  
Extra Dimensions ◽  
Field Potential ◽  
Internal Symmetry ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Generate Vector ◽  
Higgs Effect ◽  
Goldstone Modes

We study emergent Yang–Mills theories which could origin from universal extra dimensions. Particularly, some vector field potential terms or polynomial vector field constraints introduced into five-dimensional (5D) non-Abelian gauge theory is shown to lead to spontaneous violation of an underlying spacetime symmetry and generate vector pseudo-Goldstone modes as conventional four-dimensional (4D) gauge boson candidates. As a special signature, apart from conventional gauge couplings, there appear an infinite number of the properly suppressed direct multi-boson (multi-photon in particular) interaction couplings in emergent Yang–Mills theories whose observation could shed light on their high-dimensional nature. Moreover, in these theories, an internal symmetry also appeared spontaneously broken to its diagonal subgroups. This breaking originates from the extra vector field components playing the role of some adjoint scalar field multiplet in the 4D spacetime. So, one naturally has the Higgs effect without a specially introduced scalar field multiplet. Remarkably, when applied to Grand Unified Theories (GUTs), this results in an automatic breakdown of emergent GUTs down to the Standard Model (SM) just at the 5D Lorentz violation scale M.

scholarly journals Magnetic Catalysis of Chiral Symmetry Breaking: A Holographic Prospective

2010 ◽  
Vol 2010 ◽  
pp. 1-56 ◽  
Author(s):  
Veselin Filev ◽  
Radoslav Rashkov
Keyword(s):  
Chiral Symmetry Breaking ◽  
Energy Levels ◽  
Zeeman Splitting ◽  
Internal Symmetry ◽  
Spontaneous Breaking ◽  
Mass Generation ◽  
Yang Mills ◽  
Magnetic Catalysis ◽  
Analytic Derivation ◽  
Goldstone Modes

We review a recent investigation of the effect of magnetic catalysis of mass generation in holographic Yang-Mills theories. We aim at a self-contained and pedagogical form of the review. We provide a brief field theory background and review the basics of holographic flavordynamics. The main part of the paper investigates the influence of external magnetic field to holographic gauge theories dual to the D3/D5- and D3/D7-brane intersections. Among the observed phenomena are the spontaneous breaking of a global internal symmetry, Zeeman splitting of the energy levels, and the existence of pseudo, Goldstone modes. An analytic derivation of the Gell-Mann-Oaks-Renner relation for the D3/D7 set up is reviewed. In the D3/D5 case, the pseudo-Goldstone modes satisfy nonrelativistic dispersion relation. The studies reviewed confirm the universal nature of the magnetic catalysis of mass generation.

scholarly journals NON-ABELIAN GAUGE SYMMETRIES INDUCED BY THE UNOBSERVABILITY OF EXTRA DIMENSIONS IN A KALUZA–KLEIN APPROACH

2006 ◽  
Vol 21 (03) ◽  
pp. 265-274 ◽  
Author(s):  
FRANCESCO CIANFRANI ◽  
GIOVANNI MONTANI
Keyword(s):  
Extra Dimensions ◽  
Gauge Coupling ◽  
Einstein Equations ◽  
Field Equations ◽  
Abelian Gauge ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Gauge Symmetries ◽  
The Right ◽  
Kaluza Klein

In this work we deal with the extension of the Kaluza–Klein approach to a non-Abelian gauge theory; we show how we need to consider the link between the n-dimensional model and a four-dimensional observer physics, in order to reproduce field equations and gauge transformations in the four-dimensional picture. More precisely, in field equations any dependence on extra coordinates is canceled out by an integration, as consequence of the unobservability of extra dimensions. Thus, by virtue of this extra dimension unobservability, we are able to recast the multidimensional Einstein equations into the four-dimensional Einstein–Yang–Mills ones, as well as all the right gauge transformations of fields are induced. The same analysis is performed for the Dirac equation describing the dynamics of the matter fields and, again, the gauge coupling with Yang–Mills fields are inferred from the multidimensional free fields theory, together with the proper spinors transformations.

scholarly journals The gluon condensate in an effective SU(2) Yang–Mills theory

2019 ◽  
Vol 34 (02) ◽  
pp. 1950018
Author(s):  
A. N. Efremov
Keyword(s):  
Renormalization Group ◽  
Scalar Field ◽  
Gluon Condensate ◽  
Energy Scale ◽  
Low Energy ◽  
Effective Theory ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Mexican Hat ◽  
Text Model

We make progress towards a derivation of a low energy effective theory for SU(2) Yang–Mills theory. This low energy action is computed to 1-loop using the renormalization group technique, taking proper care of the Slavnov–Taylor identities in the Maximal Abelian Gauge. After that, we perform the Spin-Charge decomposition in a way proposed by Faddeev and Niemi. The resulting action describes a pair of nonlinear O(3) and [Formula: see text]-models interacting with a scalar field. The potential of the scalar field is a Mexican hat and the location of the minima sets the energy scale of solitonic configurations of the [Formula: see text]-model fields whose excitations correspond to glueball states.

Abelian gauge theories: The framework of quantum electrodynamics (QED)

2021 ◽  
pp. 507-547
Author(s):  
Jean Zinn-Justin
Keyword(s):  
Field Theory ◽  
Gauge Theory ◽  
Vector Field ◽  
Scalar Field ◽  
Quantum Electrodynamics ◽  
Particle Physics ◽  
Gauge Theories ◽  
Abelian Gauge ◽  
Four Dimensions ◽  
Gauge Fixing

This chapter is devoted Abelian gauge theory, whose physical realization is quantum electrodynamics (QED). Since many textbooks deal extensively with QED, the chapter focusses mainly on the more formal properties of Abelian gauge theories. First, the free massive vector field is considered, because its quantization does not immediately follow from the quantization of the scalar field, and thus requires a specific analysis. If the vector field is coupled to a conserved current, it is possible to construct a field theory with fermion matter renormalizable in four dimensions. In this case, a massless vector limit can be defined, and the corresponding field theory is gauge invariant. To directly quantize a gauge theory starting directly from first principles, it is necessary to introduce gauge fixing. The formal equivalence between different gauges is established. The Abelian gauge symmetry, broken by gauge-fixing terms, leads to a set of Ward–Takahashi (WT) identities which are used to prove the renormalizability of the quantum field theory (QFT). Renormalization group (RG) equations follow, and the RG β-function is calculated at leading order. As an introduction to the Standard Model of particle physics, the Abelian Landau–Ginzburg–Higgs model is described, where the gauge field is coupled to a complex scalar field with a non-zero expectation value, leading to a model that classically also describes a superconductor in a magnetic field.

scholarly journals Increasing Potentials in Classical Non-Abelian and Abelian Gauge Theories

1997 ◽  
Vol 12 (26) ◽  
pp. 4823-4830 ◽  
Author(s):  
D. Singleton ◽  
A. Yoshida
Keyword(s):  
Exact Solution ◽  
Electromagnetic Field ◽  
Scalar Field ◽  
Coulomb Potential ◽  
Gauge Theories ◽  
Field Energy ◽  
Infinite Field ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Mills Field

An exact solution for an SU(2) Yang–Mills field coupled to a scalar field is given, which has potentials with linear, 1/r and 1/r2 parts. This may be of some interest since some phenomenological QCD studies assume a linear plus Coulomb potential. We also show that in the Nielsen–Olesen Abelian model there is an exact solution in the BPS limit, which has a 1/r electromagnetic field and a logarithmically rising scalar field. Both of these solutions must be cutoff from above to avoid infinite field energy.

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 CHAOTIC INFLATION ON THE RANDALL–SUNDRUM TWO-BRANE MODEL

2010 ◽  
Vol 25 (31) ◽  
pp. 2697-2713
Author(s):  
KOUROSH NOZARI ◽  
SIAMAK AKHSHABI
Keyword(s):  
Scalar Field ◽  
Field Potential ◽  
Friedmann Equation ◽  
Warp Factor ◽  
Model Parameters ◽  
Stabilization Mechanism ◽  
Brane Model ◽  
Inflation Model ◽  
Bulk Scalar Field ◽  
Chaotic Inflation

We construct an inflation model on the Randall–Sundrum I (RSI) brane where a bulk scalar field stabilizes the inter-brane separation. We study impact of the bulk scalar field on the inflationary dynamics on the brane. We proceed in two different approaches: in the first approach, the stabilizing field potential is directly appeared in the Friedmann equation and the resulting scenario is effectively a two-field inflation. In the second approach, the stabilization mechanism is considered in the context of a warp factor so that there is just one field present that plays the roles of both inflaton and stabilizer. We study constraints imposed on the model parameters from recent observations.

ANTI-SELF-DUAL SOLUTIONS OF THE YANG-MILLS EQUATIONS IN 4n DIMENSIONS

1992 ◽  
Vol 07 (23) ◽  
pp. 2077-2085 ◽  
Author(s):  
A. D. POPOV
Keyword(s):  
Scalar Field ◽  
Euclidean Space ◽  
Lie Algebra ◽  
Linear Equations ◽  
Dual Solutions ◽  
Gauge Fields ◽  
System Of Equations ◽  
Semisimple Lie Algebra ◽  
Yang Mills ◽  
Self Duality

The anti-self-duality equations for gauge fields in d = 4 and a generalization of these equations to dimension d = 4n are considered. For gauge fields with values in an arbitrary semisimple Lie algebra [Formula: see text] we introduce the ansatz which reduces the anti-self-duality equations in the Euclidean space ℝ4n to a system of equations breaking up into the well known Nahm's equations and some linear equations for scalar field φ.

scholarly journals Cohomological localization of $$ \mathcal{N} $$ = 2 gauge theories with matter

2020 ◽  
Vol 2020 (9) ◽  
Author(s):  
Guido Festuccia ◽  
Anastasios Gorantis ◽  
Antonio Pittelli ◽  
Konstantina Polydorou ◽  
Lorenzo Ruggeri
Keyword(s):  
Vector Field ◽  
Extended Supersymmetry ◽  
General Framework ◽  
Gauge Theories ◽  
Killing Vector ◽  
Killing Vector Field ◽  
Explicit Result ◽  
Yang Mills ◽  
Self Duality ◽  
Witten Theory

Abstract We construct a large class of gauge theories with extended supersymmetry on four-dimensional manifolds with a Killing vector field and isolated fixed points. We extend previous results limited to super Yang-Mills theory to general $$ \mathcal{N} $$ N = 2 gauge theories including hypermultiplets. We present a general framework encompassing equivariant Donaldson-Witten theory and Pestun’s theory on S4 as two particular cases. This is achieved by expressing fields in cohomological variables, whose features are dictated by supersymmetry and require a generalized notion of self-duality for two-forms and of chirality for spinors. Finally, we implement localization techniques to compute the exact partition function of the cohomological theories we built up and write the explicit result for manifolds with diverse topologies.

scholarly journals FERMIONS IN THE BACKGROUND OF DILATONIC SPHALERONS

1994 ◽  
Vol 09 (40) ◽  
pp. 3731-3739 ◽  
Author(s):  
GEORGE LAVRELASHVILI
Keyword(s):  
Gauge Field ◽  
Field Potential ◽  
Spherically Symmetric ◽  
Yang Mills ◽  
Zero Modes ◽  
Discrete Sequence ◽  
Number Of Zeros ◽  
Spherically Symmetric Solutions ◽  
Static Spherically Symmetric Solutions

We discuss the properties and interpretation of a discrete sequence of a static spherically symmetric solutions of the Yang-Mills dilaton theory. This sequence is parametrized by the number of zeros, n, of a component of the gauge field potential. It is demonstrated that solutions with odd n possess all the properties of the sphaleron. It is shown that there are normalizable fermion zero modes in the background of these solutions. The question of instability is critically analyzed.

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