Aharonov--Bohm Effect in 3D Abelian Higgs Theory

We study a field--theoretical analogue of the Aharonov--Bohm effect in the 3D Abelian Higgs Model: the corresponding topological interaction is proportional to the linking number of the vortex and the particle world trajectories. We show that the Aharonov--Bohm effect gives rise to a nontrivial interaction of tested charged particles.Comment: LaTeX, 3 pages, 1 figure, uses epsf.sty; talk presented at LATTICE96(topology), St. Louis, US

Properties of the Abelian Projection Fields in SU(N)SU(N) Lattice Gluodynamics

't~Hooft's abelian projection of $SU(N)$ gauge theory yields $N$ mutually constrained, compact abelian fields which are permutationally equivalent. We formulate the notion of ``species permutation'' symmetry of the $N$ abelian projection fields and discuss its consequences for cross-species correlators. We show that at large $N$ cross-species interactions are ${1\over N}$ suppressed relative to same-species interactions. Numerical simulations at $N=3$ support our symmetry arguments and reveal the existence of inter-species interactions of size {\cal O\/}\bigl({1\over N-1}\bigr) as analytically predicted.Comment: 13 pages, 1 postscript figure include

Strings and Aharonov-Bohm Effect in Abelian Higgs Model

We investigate numerically the properties of the Abrikosov-Nielsen-Olesen strings in 4D abelian Higgs model. The fractal dimension D_f of the vortex strings was found to be large in the Coulomb phase and it is close to 2 in the Higgs phase. We also show that the Wilson loop for non-integer charges is correlated with the linking number of the vortex string world sheets and the test particle world trajectory. We find that this topological (Aharonov-Bohm) interaction gives the main contribution to the Wilson loop quantum average for non-integer test charges in the vicinity of the Coulomb-Higgs phase transition.Comment: 8 pages, LaTeX, 5 EPS-figures, uses epsf.st

Finite-temperature chiral condensate and low-lying Dirac eigenvalues in quenched SU(2) lattice gauge theory

The spectrum of low-lying eigenvalues of overlap Dirac operator in quenched SU(2) lattice gauge theory with tadpole-improved Symanzik action is studied at finite temperatures in the vicinity of the confinement-deconfinement phase transition defined by the expectation value of the Polyakov line. The value of the chiral condensate obtained from the Banks-Casher relation is found to drop down rapidly at T = Tc, though not going to zero. At Tc' = 1.5 Tc = 480 MeV the chiral condensate decreases rapidly one again and becomes either very small or zero. At T < Tc the distributions of small eigenvalues are universal and are well described by chiral orthogonal ensemble of random matrices. In the temperature range above Tc where both the chiral condensate and the expectation value of the Polyakov line are nonzero the distributions of small eigenvalues are not universal. Here the eigenvalue spectrum is better described by a phenomenological model of dilute instanton - anti-instanton gas.Comment: 8 pages RevTeX, 5 figures, 2 table

Demons and Abelian Projection QCD: Action and Crossover

I evaluate S_{APQCD}, the exact action of Abelian projection QCD, using the microcanonical demon method. Starting with a trial action consisting of L=1, L=2, & L=3 LxL plaquettes plus a Smit-van-der-Sijs magnetic monopole ``mass'' operator, I show that coefficients of the L=2 and L=3 plaquettes vanish at all beta_{SU2}. In fact, at strong coupling S_{APQCD} is essentially the 1x1 compact QED action with beta_{U1}=beta_{SU2}/2. Beyond beta_{SU2}>=2, S_{APQCD} gains an exogenous negative 1x1x1 magnetic monopole mass shift. Note that my approach differs fundamentally from the Smit-van-der-Sijs approach in that I do not make an a priori assumption about monopole or plaquette size in S_{APQCD}. Indeed, these results suggest that QCD monopoles are pointlike, in contrast to the ``effective'' condensation picture put forth by Smit and van der Sijs.Comment: to appear in Physics Letters B347 (1995) 367-37