scholarly journals Yang-Mills theory as a deformation of topological field theory, dimensional reduction, and quark confinement

1998 ◽  
Vol 58 (10) ◽  
Author(s):  
Kei-Ichi Kondo
Keyword(s):  
Field Theory ◽  
Dimensional Reduction ◽  
Topological Field Theory ◽  
Quark Confinement ◽  
Yang Mills ◽  
Topological Field

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.

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.

scholarly journals DIMENSIONAL REDUCTION OF DUAL TOPOLOGICAL THEORIES

1996 ◽  
Vol 11 (22) ◽  
pp. 1777-1784 ◽  
Author(s):  
KASPER OLSEN
Keyword(s):  
Field Theory ◽  
Dimensional Reduction ◽  
Two Dimensions ◽  
Topological Field Theory ◽  
Witten Theory ◽  
Topological Field ◽  
Topological Theories

We describe the reduction from four to two dimensions of the SU(2) Donaldson–Witten theory and the dual twisted Seiberg–Witten theory, i.e. the Abelian topological field theory corresponding to the Seiberg–Witten monopole equations.

A COMMENT ON TOPOLOGICAL FIELD THEORY QUANTIZATION AND STOCHASTIC PROCESSES

1990 ◽  
Vol 05 (19) ◽  
pp. 3777-3786 ◽  
Author(s):  
L.F. CUGLIANDOLO ◽  
G. LOZANO ◽  
H. MONTANI ◽  
F.A. SCHAPOSNIK
Keyword(s):  
Field Theory ◽  
Equilibrium State ◽  
Stochastic Processes ◽  
Topological Field Theories ◽  
Topological Charge ◽  
Field Theories ◽  
Langevin Equations ◽  
Topological Field Theory ◽  
Topological Field

We discuss the relation between different quantization approaches to topological field theories by deriving a connection between Bogomol’nyi and Langevin equations for stochastic processes which evolve towards an equilibrium state governed by the topological charge.

TETRAHEDRA AND POLYNOMIAL EQUATIONS IN TOPOLOGICAL FIELD THEORY

1991 ◽  
Vol 06 (20) ◽  
pp. 3571-3598 ◽  
Author(s):  
NOUREDDINE CHAIR ◽  
CHUAN-JIE ZHU
Keyword(s):  
Field Theory ◽  
Topological Field Theory ◽  
Fundamental Representation ◽  
Conformal Blocks ◽  
Conformal Field ◽  
Witten Theory ◽  
Topological Field ◽  
General Program ◽  
The One ◽  
Chern Simons

Some tetrahedra in SUk(2) Chern-Simons-Witten theory are computed. The results can be used to compute an arbitrary tetrahedron inductively by fusing with the fundamental representation. The results obtained are in agreement with those of quantum groups. By associating a (finite) topological field theory (FTFT) to every rational conformal field theory (RCFT), we show that the pentagon and hexagon equations in RCFT follow directly from some skein relations in FTFT. By generalizing the operation of surgery on links in FTFT, we also derive an explicit expression for the modular transformation matrix S(k) of the one-point conformal blocks on a torus in RCFT and the equations satisfied by S(k), in agreement with those required in RCFT. The implication of our results on the general program of classifying RCFT is also discussed.

scholarly journals Chern–Simons–Rozansky–Witten topological field theory

2009 ◽  
Vol 823 (3) ◽  
pp. 403-427 ◽  
Author(s):  
Anton Kapustin ◽  
Natalia Saulina
Keyword(s):  
Field Theory ◽  
Topological Field Theory ◽  
Topological Field ◽  
Chern Simons
Sign in / Sign up

Export Citation Format

Share Document