scholarly journals Renormalizable Abelian-Projected Effective Gauge Theory Derived from Quantum Chromodynamics II

2003 ◽  
Vol 18 (20) ◽  
pp. 1403-1412 ◽  
Author(s):  
Toru Shinohara
Keyword(s):  
Gauge Theory ◽  
Tensor Field ◽  
Anomalous Dimension ◽  
Low Energy ◽  
Effective Theory ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Antisymmetric Tensor Field ◽  
Group Functions ◽  
Multiplicative Renormalizability

In the previous paper,1 we derived the Abelian projected effective gauge theory as a low energy effective theory of the SU (N) Yang–Mills theory by adopting the maximal Abelian gauge. At that time, we have demonstrated the multiplicative renormalizability of the propagators for the diagonal gluon and the dual Abelian antisymmetric tensor field. In this paper, we show the multiplicative renormalizability of the Green's functions also for the off-diagonal gluon. Moreover, we complement the previous results by calculating the anomalous dimension and the renormalization group functions which are undetermined in the previous paper.

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.

scholarly journals Superfield approach to nilpotent symmetries in 3D Jackiw–Pi model of massive non-Abelian theory

2014 ◽  
Vol 92 (9) ◽  
pp. 1033-1042 ◽  
Author(s):  
S. Gupta ◽  
R. Kumar ◽  
R.P. Malik
Keyword(s):  
Gauge Theory ◽  
Brst Symmetry ◽  
Point Of View ◽  
Abelian Gauge ◽  
Gauge Invariant ◽  
Abelian Gauge Theory ◽  
Gauge Transformations ◽  
Yang Mills ◽  
Symmetry Transformations ◽  
Augmented Superfield Formalism

In the available literature, only the Becchi–Rouet–Stora–Tyutin (BRST) symmetries are known for the Jackiw–Pi model of the three (2 + 1)-dimensional (3D) massive non-Abelian gauge theory. We derive the off-shell nilpotent [Formula: see text] and absolutely anticommuting (sbsab + sabsb = 0) (anti-)BRST transformations s(a)b corresponding to the usual Yang–Mills gauge transformations of this model by exploiting the “augmented” superfield formalism where the horizontality condition and gauge invariant restrictions blend together in a meaningful manner. There is a non-Yang–Mills (NYM) symmetry in this theory, too. However, we do not touch the NYM symmetry in our present endeavor. This superfield formalism leads to the derivation of an (anti-)BRST invariant Curci–Ferrari restriction, which plays a key role in the proof of absolute anticommutativity of s(a)b. The derivation of the proper anti-BRST symmetry transformations is important from the point of view of geometrical objects called gerbes. A novel feature of our present investigation is the derivation of the (anti-)BRST transformations for the auxiliary field ρ from our superfield formalism, which is neither generated by the (anti-)BRST charges nor obtained from the requirements of nilpotency and (or) absolute anticommutativity of the (anti-)BRST symmetries for our present 3D non-Abelian 1-form gauge theory.

scholarly journals A Yang–Mills Theory in Loop Space and Chapline–Manton Coupling

1997 ◽  
Vol 12 (02) ◽  
pp. 111-119 ◽  
Author(s):  
Shinichi Deguchi ◽  
Tadahito Nakajima
Keyword(s):  
Field Theory ◽  
Local Field ◽  
Loop Space ◽  
Tensor Field ◽  
Symmetric Tensor ◽  
Tensor Fields ◽  
Yang Mills ◽  
Local Field Theory ◽  
Antisymmetric Tensor Field ◽  
Chern Simons

We consider a Yang–Mills theory in loop space with the affine gauge group. From this theory, we derive a local field theory with Yang–Mills fields and Abelian antisymmetric and symmetric tensor fields of the second rank. The Chapline–Manton coupling, i.e. coupling of Yang–Mills fields and a second-rank antisymmetric tensor field via the Chern–Simons three-form is obtained systematically.

scholarly journals DUALITY IN SUPERSYMMETRIC YANG–MILLS AND THE QUANTUM HALL EFFECT

2006 ◽  
Vol 21 (20) ◽  
pp. 1567-1585
Author(s):  
BRIAN P. DOLAN
Keyword(s):  
Gauge Theory ◽  
Hall Effect ◽  
Experimental Evidence ◽  
Quantum Hall Effect ◽  
Modular Group ◽  
Quantum Hall ◽  
Low Energy ◽  
Kinetic Term ◽  
Yang Mills ◽  
Topological Parameter

The evidence for the parallel rôles played by the modular group in [Formula: see text] supersymmetric Yang–Mills in (3+1) dimensions and the quantum Hall effect in (2+1) dimensions is reviewed. In both cases a subgroup of the full modular group acts as a map between different low energy phases of the theory, parametrised by a complex parameter in the upper-half-complex plane whose real part is a topological parameter and whose imaginary part is the coupling associated the kinetic term of the effective U(1) gauge theory. In the case of the quantum Hall effect experimental evidence in favour of the modular action is also reviewed.

scholarly journals LOOP VARIABLES WITH CHAN–PATON FACTORS

2004 ◽  
Vol 19 (01) ◽  
pp. 59-70 ◽  
Author(s):  
B. SATHIAPALAN
Keyword(s):  
Gauge Invariance ◽  
Continuum Limit ◽  
Open String ◽  
Equation Of Motion ◽  
Low Energy ◽  
Scale Transformation ◽  
Abelian Gauge ◽  
Rotation Symmetry ◽  
Yang Mills ◽  
Massless Fields

The loop variable method that has been developed for the U(1) bosonic open string is generalized to include non-Abelian gauge invariance by incorporating "Chan–Paton" gauge group indices. The scale transformation symmetry k(s)→λ(s)k(s) that was responsible for gauge invariance in the U(1) case continues to be a symmetry. In addition there is a non-Abelian "rotation" symmetry. Both symmetries crucially involve the massive modes. However, it is plausible that only a linear combination, which is the usual Yang–Mills transformation on massless fields, has a smooth (worldsheet) continuum limit. We also illustrate how an infinite number of terms in the equation of motion in the cutoff theory add up to give a term that has a smooth continuum limit, and thus contributes to the low energy Yang–Mills equation of motion.

Yang–Mills gauge theory and Higgs particle

2015 ◽  
Vol 30 (34) ◽  
pp. 1530065
Author(s):  
Tai Tsun Wu ◽  
Sau Lan Wu
Keyword(s):  
Experimental Data ◽  
Gauge Theory ◽  
Standard Model ◽  
Atlas Collaboration ◽  
Higgs Particle ◽  
Abelian Gauge ◽  
Yang Mills ◽  
The Right ◽  
The Masses

Motivated by the experimental data on the Higgs particle from the ATLAS Collaboration and the CMS Collaboration at CERN, the standard model, which is a Yang–Mills non-Abelian gauge theory with the group [Formula: see text], is augmented by scalar quarks and scalar leptons without changing the gauge group and without any additional Higgs particle. Thus there is fermion–boson symmetry between these new particles and the known quarks and leptons. In a simplest scenario, the cancellation of the quadratic divergences in this augmented standard model leads to a determination of the masses of all these scalar quarks and scalar leptons. All these masses are found to be less than 100 GeV/c2, and the right-handed scalar neutrinos are especially light. Alterative procedures are given with less reliance on the experimental data, leading to the same conclusions.

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.

scholarly journals A SUPERSPACE FORMULATION OF ABELIAN ANTISYMMETRIC TENSOR GAUGE THEORY

2000 ◽  
Vol 15 (15) ◽  
pp. 965-978 ◽  
Author(s):  
SHINICHI DEGUCHI ◽  
BHABANI PRASAD MANDAL
Keyword(s):  
Gauge Theory ◽  
Tensor Field ◽  
Ad Hoc ◽  
Compact Form ◽  
Antisymmetric Tensor ◽  
Lagrange Equations ◽  
Generating Functional ◽  
Transformation Rules ◽  
Antisymmetric Tensor Field ◽  
Rank 2

We apply a superspace formulation to the four-dimensional gauge theory of a massless Abelian antisymmetric tensor field of rank 2. The theory is formulated in a six-dimensional superspace using rank-2 tensor, vector and scalar superfields and their associated supersources. It is shown that BRS transformation rules of fields are realized as Euler–Lagrange equations without assuming the so-called horizontality condition in an ad hoc manner and that a generating functional [Formula: see text] constructed in the superspace reduces to that of the ordinary gauge theory of Abelian rank-2 antisymmetric tensor field. The WT identity for this theory is derived by making use of the superspace formulation and is expressed in a neat and compact form [Formula: see text].

scholarly journals Condensation of p-Branes and Generalized Higgs/Confinement Duality

1997 ◽  
Vol 12 (06) ◽  
pp. 1227-1235 ◽  
Author(s):  
Fernando Quevedo ◽  
Carlo A. Trugenberger
Keyword(s):  
Phase Transition ◽  
Recent Work ◽  
Finite Temperature ◽  
Weak Coupling ◽  
Tensor Field ◽  
Low Energy ◽  
Field Theories ◽  
Antisymmetric Tensor ◽  
Antisymmetric Tensor Field

We review our recent work on the low-energy actions and the realizations of strong-weak coupling dualities in non-perturbative phases of compact antisymmetric tensor field theories due to p-brane condensation. As examples we derive and discuss the confining string and confining membrane actions obtained from compact vector and tensor theories in 4D. We also mention the relevance of our results for the description of the Hagedorn phase transition of finite temperature strings.

scholarly journals GAUGE INVARIANCES IN THE PROCA MODEL

1998 ◽  
Vol 13 (05) ◽  
pp. 765-778 ◽  
Author(s):  
A. S. VYTHEESWARAN
Keyword(s):  
Gauge Theory ◽  
Phase Space ◽  
Projection Operator ◽  
Tensor Field ◽  
Gauge Theories ◽  
Lorentz Invariance ◽  
Maxwell Field ◽  
Antisymmetric Tensor ◽  
Antisymmetric Tensor Field

We show that the Abelian Proca model, which is gauge noninvariant with second class constraints can be converted into gauge theories with first class constraints. The method used, which we call gauge unfixing, employs a projection operator defined in the original phase space. This operator can be constructed in more than one way and so we get more than one gauge theory. Two such gauge theories are the Stückelberg theory and the theory of Maxwell field interacting with an antisymmetric tensor field. We also show that the application of the projection operator does not affect the Lorentz invariance of this model.

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