scholarly journals NON-ABELIAN STOKES THEOREM AND QUARK CONFINEMENT IN SU(3) YANG–MILLS GAUGE THEORY

2000 ◽  
Vol 15 (05) ◽  
pp. 367-377 ◽  
Author(s):  
KEI-ICHI KONDO ◽  
YUTARO TAIRA
Keyword(s):  
Magnetic Monopole ◽  
Dominant Role ◽  
Topological Field Theory ◽  
Quark Confinement ◽  
Forthcoming Article ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Gauge Fixing ◽  
Topological Field ◽  
Area Law

We derive a new version of SU (3) non-Abelian Stokes theorem by making use of the coherent state representation on the coset space SU (3)/ U (1) × U (1)) = F2, the flag space. Then we outline a derivation of the area law of the Wilson loop in SU (3) Yang–Mills theory in the maximal Abelian gauge (the detailed exposition will be given in a forthcoming article). This derivation is performed by combining the non-Abelian Stokes theorem with the reformulation of the Yang–Mills theory as a perturbative deformation of a topological field theory recently proposed by one of the authors. Within this framework, we show that the fundamental quark is confined even if G = SU (3) is broken by partial gauge fixing into H = U (2) just as G is broken to H = U(1) × U(1). An origin of the area law is related to the geometric phase of the Wilczek–Zee holonomy for U (2). Abelian dominance is an immediate by-product of these results and magnetic monopole plays the dominant role in this derivation.

FLUCTONS

2008 ◽  
Vol 05 (03) ◽  
pp. 375-386 ◽  
Author(s):  
R. CARTAS-FUENTEVILLA ◽  
J. M. SOLANO-ALTAMIRANO
Keyword(s):  
Degrees Of Freedom ◽  
Index Theorem ◽  
Quantum Mechanical ◽  
Topological Field Theory ◽  
Topological Phases ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Topological Field ◽  
Dual Domain ◽  
Topological Fluctuations

From the perspective of topological field theory we explore the physics beyond instantons. We propose the fluctons as nonperturbative topological fluctuations of vacuum, from which the self-dual domain of instantons is attained as a particular case. Invoking the Atiyah–Singer index theorem, we determine the dimension of the corresponding flucton moduli space, which gives the number of degrees of freedom of the fluctons. An important consequence of these results is that the topological phases of vacuum in non-Abelian gauge theories are not necessarily associated with self-dual fields, but only with smooth fields. Fluctons in different scenarios are considered, the basic aspects of the quantum mechanical amplitude for fluctons are discussed. A possible application of fluctons in the N = 4 Topologically Twisted Supersymmetric Yang–Mills Theory is explored and the case of gravity is discussed briefly.

scholarly journals A FORMULATION OF THE YANG–MILLS THEORY AS A DEFORMATION OF A TOPOLOGICAL FIELD THEORY BASED ON THE BACKGROUND FIELD METHOD AND QUARK CONFINEMENT PROBLEM

2001 ◽  
Vol 16 (07) ◽  
pp. 1303-1346 ◽  
Author(s):  
KEI-ICHI KONDO
Keyword(s):  
Field Theory ◽  
Magnetic Monopole ◽  
Background Field ◽  
Field Method ◽  
Quark Confinement ◽  
Mass Generation ◽  
Yang Mills ◽  
Topological Quantum ◽  
Gauge Fixing ◽  
Background Field Method

By making use of the background field method, we derive a novel reformulation of the Yang–Mills theory which was proposed recently by the author to derive quark confinement in QCD. This reformulation identifies the Yang–Mills theory with a deformation of a topological quantum field theory. The relevant background is given by the topologically nontrivial field configuration, especially, the topological soliton which can be identified with the magnetic monopole current in four dimensions. We argue that the gauge fixing term becomes dynamical and that the gluon mass generation takes place by a spontaneous breakdown of the hidden supersymmetry caused by the dimensional reduction. We also propose a numerical simulation to confirm the validity of the scheme we have proposed. Finally we point out that the gauge fixing part may have a geometric meaning from the viewpoint of global topology where the magnetic monopole solution represents the critical point of a Morse function in the space of field configurations.

scholarly journals SUPERSYMMETRIC YANG–MILLS THEORIES WITH EXACT SUPERSYMMETRY ON THE LATTICE

2011 ◽  
Vol 26 (30n31) ◽  
pp. 5057-5132 ◽  
Author(s):  
ANOSH JOSEPH
Keyword(s):  
Field Theory ◽  
Euclidean Space ◽  
Topological Field Theory ◽  
Strongly Coupled ◽  
Dimensional Lattice ◽  
Yang Mills ◽  
Gravitational Theories ◽  
Topological Field ◽  
Perturbative Renormalization ◽  
The One

Inspired by the ideas from topological field theory it is possible to rewrite the supersymmetric charges of certain classes of extended supersymmetric Yang–Mills (SYM) theories in such a way that they are compatible with the discretization on a Euclidean space–time lattice. Such theories are known as maximally twisted SYM theories. In this review we discuss the construction and some applications of such classes of theories. The one-loop perturbative renormalization of the four-dimensional lattice [Formula: see text] SYM is discussed in particular. The lattice theories constructed using twisted approach play an important role in investigating the thermal phases of strongly coupled SYM theories and also the thermodynamic properties of their dual gravitational theories.

GAUGE FIXING TOPOLOGICAL YANG-MILLS

1990 ◽  
Vol 05 (07) ◽  
pp. 1369-1381 ◽  
Author(s):  
ROBERT MYERS
Keyword(s):  
Gauge Symmetry ◽  
Topological Field Theories ◽  
Correlation Functions ◽  
Field Theories ◽  
Yang Mills ◽  
Gauge Fixing ◽  
Topological Field ◽  
Topological Gravity

We examine two methods of fixing the gauge symmetry in Witten’s topological Yang-Mills theory. We find that both procedures produce the same nontrivial correlation functions. Our results also apply to other topological field theories, such as topological gravity.

scholarly journals EMERGENCE OF THE HAAR MEASURE IN THE STANDARD FUNCTIONAL INTEGRAL REPRESENTATION OF THE YANG-MILLS PARTITION FUNCTION

1996 ◽  
Vol 11 (30) ◽  
pp. 2451-2461 ◽  
Author(s):  
H. REINHARDT
Keyword(s):  
Partition Function ◽  
Path Integral ◽  
Haar Measure ◽  
Transition Amplitude ◽  
Functional Integral ◽  
Abelian Gauge ◽  
Gauge Invariant ◽  
Yang Mills ◽  
Gauge Fixing ◽  
Popov Method

The conventional path integral expression for the Yang–Mills transition amplitude with flat measure and gauge-fixing built in via the Faddeev-Popov method has been claimed to fall short of guaranteeing gauge invariance in the nonperturbative regime. We show, however, that it yields the gauge-invariant partition function where the projection onto gauge-invariant wave functions is explicitly performed by integrating over the compact gauge group. In a variant of maximal Abelian gauge the Haar measure arises in the conventional Yang-Mills path integral from the Faddeev-Popov determinant.

scholarly journals Abelian Projection of Massive SU(2) Yang–Mills Theory

2003 ◽  
Vol 18 (29) ◽  
pp. 2051-2070 ◽  
Author(s):  
Shinichi Deguchi ◽  
Yousuke Kokubo
Keyword(s):  
Distance Scale ◽  
Static Potential ◽  
Long Distance ◽  
Abelian Gauge ◽  
Yang Mills ◽  
Longitudinal Modes ◽  
Gauge Fixing ◽  
Mass Terms ◽  
Faddeev Model ◽  
Modified Theory

We derive an effective Abelian gauge theory (EAGT) of a modified SU(2) Yang–Mills theory. The modification is made by explicitly introducing mass terms of the off-diagonal gluon fields into pure SU(2) Yang–Mills theory, in order that Abelian dominance at a long-distance scale is realized in the modified theory. In deriving the EAGT, the off-diagonal gluon fields involving longitudinal modes are treated as fields that produce quantum effects on the diagonal gluon field and other fields relevant at a long-distance scale. Unlike earlier papers, a necessary gauge fixing is carried out without spoiling the global SU(2) gauge symmetry. We show that the EAGT allows a composite of the Yukawa and the linear potentials which also occurs in an extended dual Abelian Higgs model. This composite potential is understood to be a static potential between color-electric charges. In addition, we point out that the EAGT involves the Skyrme–Faddeev model.

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