Dual variables for lattice gauge theories and the phase structure ofZ(N)systems

Abstract

The 't Hooft disorder parameters are constructed within the framework of SU(N) lattice gauge theories in three or four dimensions. It is found that these operators arise naturally from a duality transformation which is simllar to the standard transformation for Z(N) gauge theories. To illustrate the behavior of dual variables in a simpler context, we study the Villain form of the Z(N) gauge system in three and four dimensions. The techniques include duality, strong-coupling expansions, and the electrodynamic representation. In four dimensions it is found that for N > N, -4, the system possesses at least three phases: a strong-coupling phase with electric confinement, a weak-coupling phase with magnetic confinement, and an intermediate phase which resembles QED, with a massless photon and no confinement. We also study an SU(N)-Hlggs system, which interpolates between the Z(N) and SU(N) systems.

A euclidean lattice construction of supersymmetric Yang-Mills theories with sixteen supercharges

“…[39] in order to try to shed light on the fascinating dualities present in N = 4 SYM theory in four [3] and three [40 -42] dimensions.…”

Local discrete symmetry and quantum-mechanical hair

“…Since there is a duality transformation that interchanges strong and weak coupling in this model [26,28], the weak-coupling expansion also has a finite radius of convergence. At weak coupling, the leading nontrivial contribution to The leading contribution to (F(I)W(C)~at weak coupling arises from a configuration of the link variables such that none of the plaquettes dual to I are frustrated*.…”

“…We noted that F(I) is merely a gauge transformation in a pure gauge theory, and the surface I is an artifact that can be moved by means of a singular gauge transformation. The lattice analog of a singular gauge transformation is the change of variable [28] (5.10) * This construction is easier to visualize in three-dimensional euclidean space. Then .S is a closed loop made up of links of the dual lattice, and each link of X is dual to a plaquette of the original lattice.…”

Center vortex model for the infrared sector ofSU(3)Yang-Mills theory: Vortex free energy

“…As the plane P is filled up one elementary square p i at a time 6 , one can record the free energies…”

“…Also in the dual language, the change of behavior of the vortex free energy across the deconfinement phase transition can be associated with a (magnetic) center symmetry [1,4], which is broken in the low-temperature phase. Subsequent to 't Hooft's suggestion, realizations of the 't Hooft loop operator within the framework of lattice gauge theory formulated in 3+1-dimensional (Euclidean) space-time were discussed and schemes of measuring the free energies of the vortices thus introduced into the gauge configurations were devised [5,6,7,8]. On this basis, sufficient conditions for confinement via vortex condensation were established [5,9].…”