Z₂ ELECTRIC STRINGS AND CENTER VORTICES IN SU (2) LATTICE GAUGE THEORY

Abstract

We study the representations of SU (2) lattice gauge theory in terms of sums over the worldsheets of center vortices and Z2 electric strings, i.e. surfaces which open on the Wilson loop. It is shown that in contrast to center vortices the density of electric Z2 strings diverges in the continuum limit of the theory independently of the gauge fixing, however, their contribution to the Wilson loop yields physical string tension due to non-positivity of their statistical weight in the path integral, which is in turn related to the presence of Z2 topological monopoles in the theory.PACS numbers: 12.38. Aw; 11.25.Pm It is often believed that Yang-Mills theory can be entirely reformulated in terms of string degrees of freedom, since the basic property of non-Abelian gauge theories -quark confinement -is explained by the emergence of confining string which stretches between test quark and antiquark. Even the simplest string models for Yang-Mills theory turn out to be very successful in reproducing the spectrum of bound states of the theory. One of the most successful recent developments is the AdS/QCD, the description of QCD bound states in terms of string theory on five-dimensional anti-de Sitter space or its modifications [1,2]. In this description the Wilson loop behaves asis the area of the minimal surface in five-dimensional space spanned on the loop C. The loop C is assumed to lie on the boundary of this five-dimensional space. However, up to now there is no exact representation of continuum Yang-Mills theory in terms of electric strings, i.e. the strings which open on Wilson loops. In fact, the only string one usually encounters in non-Abelian gauge theories is a chromoelectric string of finite thickness at finite lattice spacing, which is observed in numerical simulations as a cylindric region with higher energy density between two test colour charges [3,4].Recently a different type of strings has been discovered in lattice gauge theories, namely, Z N magnetic strings or center vortices. Although the existence of such strings in Yang-Mills theories was predicted a long time ago [5], they have been actually observed and investigated in lattice simulations only during the last decade [6,7]. The simulations has shown that center vortices are infinitely thin and have a finite density in the continuum limit. Moreover, lattice results suggest that center vortices are the effective degrees of freedom in the infrared domain of Yang-Mills theory [6,7], since removing center vortices from lattice configurations destroys all its characteristic infrared properties, such as confinement or spontaneous breaking of chiral symmetry. Effective action of * Electronic address: polykarp@itep.ru † Electronic address: buividovich@tut.by center vortices and their geometric properties were extensively studied in [8]. Detection of center vortices in lattice configurations of gauge fields is based on the separation of SU (N ) link variables into SU (N ) /Z N variables and the variables which take values in the center of the gauge group...