Tests of the lattice index theorem

Abstract

We investigate the lattice index theorem and the localization of the zero-modes for thick classical center vortices. For non-orientable spherical vortices, the index of the overlap Dirac operator differs from the topological charge although the traces of the plaquettes deviate only by a maximum of 1.5% from trivial plaquettes. This may be related to the fact that even in Landau gauge some links of these configuration are close to the non-trivial center elements.

Chiral Symmetry Breaking from Center Vortices

“…The spherical vortex was introduced in [6] and analyzed in more detail in [7,8,9]. It is constructed with t-links in a single time slice at fixed t = t i , given by U t (x ν ) = exp (iα(| r − r 0 |) r/r · σ ), where r is the spatial part of x ν .…”

“…A similar picture to the instanton liquid model exists insofar as lumps of topological charge arise at the intersection and writhing points of vortices. The colorful, spherical SU(2) vortex was introduced in a previous article of our group [6] and may act as a prototype for this picture, as it contributes to the topological charge by its color structure, attracting a zero mode like an instanton. We show how the interplay of various topological structures from center vortices (and instantons) leads to near-zero modes, which by the Banks-Casher relation are responsible for a finite chiral condensate.…”

Colorful vortex intersections in SU(2) lattice gauge theory and their influences on chiral properties

“…Lattice simulations have shown that center vortices contribute to the topological charge via writhing, vortex intersections [33][34][35][36][37][38][39][40] and their color structure [41][42][43][44]. Vortices lead also to spontaneous χSB [45][46][47][48][49][50][51][52][53][54][55][56].…”

“…The configurations which we want to investigate in SU(2) lattice gauge theory are thick plane vortices [37,41] extending along two coordinate axes, thickness in a third coordinate direction and formulated with non-trivial links in the forth direction. One of these vortices will get a special color structure and will be smoothed in the forth direction.…”

Topological susceptibility in the SU(3) random vortex world-surface model

“…Vortex topological charge is generated by two geometrical features, namely, vortex worldsurface intersection points and vortex world-surface writhe 1 [2,[19][20][21][22]. As described further in section 4, vortex world-surfaces will, for practical purposes, be modeled as consisting of elementary squares on a hypercubic lattice.…”