Center vortices as rigid strings

Abstract

It is shown that the action associated with center vortices in SU (2) lattice gauge theory is strongly correlated with extrinsic and internal curvatures of the vortex surface and that this correlation persists in the continuum limit. Thus a good approximation for the effective vortex action is the action of rigid strings, which can reproduce some of the observed geometric properties of center vortices. It is conjectured that rigidity may be induced by some fields localized on vortices, and a model-independent test of localization is performed. Monopoles detected in the Abelian projection are discussed as natural candidates for such two-dimensional fields.

Rigidity and percolation of center vortices

“…This action differs from the action of rigid strings used in [5] by the terms quadratic in R. Although the standard dimensional analysis shows that only σ (a) and the terms linear in K and R should survive in the continuum limit, we shall see that for center vortices higherorder terms can be equally important. It is also more convenient to redefine σ (a) = a −2 σ 0 (a) = Λ 2 UV σ 0 (a).…”

“…A basic assumption of [3,5] and this work is that the average total excess of action on the vortex worldsheets is equal to the effective vortex action W e f f [Σ] obtained by integrating over all degrees of freedom in the theory except the geometry of the vortex worldsheet Σ. In general, W e f f [Σ] can include nonlocal terms, for instance, of the form R∆ −1 R, where R is the internal curvature of the vortex worldsheet and ∆ is the covariant two-dimensional Laplacian.…”

“…According to (2.2), a 2 K p takes integer values from 0 to 4. Internal curvature for lattice surfaces was defined as in [5,6]: a 2 R s = 4 − n s , where n s is the number of sites on the vortex worldsheet which are adjacent to s. Thus in contrast to [5], where both K and R were associated with lattice sites, here K is associated with vortex plaquettes and R -with lattice sites on vortex worldsheets, which yields more self-consistent results. Average excess of action per vortex plaquette ∆S p as the function of lattice spacing and extrinsic and internal curvatures (in lattice units) is plotted on Fig.…”

“…One of them is the percolation of vortex worldsheets, which can play a crucial role in the confinement mechanism (for instance, it is known that percolating vortex disappears at the deconfinement phase transition [8]). The aim of this paper is to investigate the effective vortex action in more details than in [5] and to discuss how such action can describe the emergence of percolating vortex clusters.…”

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

“…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, Z N .…”