Center vortices and Dirac eigenmodes in SU(2) lattice gauge theory

Abstract

We study the interplay between Dirac eigenmodes and center vortices in SU(2) lattice gauge theory. In particular we focus on vortex-removed configurations and compare them to an ensemble of configurations with random changes of the link variables. We show that removing the vortices destroys all zero modes and the near zero modes are no longer coupled to topological structures. The Dirac spectrum for vortex-removed configurations in many respects resembles a free spectrum thus leading to a vanishing chiral condensate. Configurations with random changes leave the topological features of the Dirac eigensystem intact. We finally show that smooth center vortex configurations give rise to zero modes and topological near zero modes.

Role of center vortices in chiral symmetry breaking in SU(3) gauge theory

“…The analogy to the SU(2) gauge group [33] is thus also broken: in SU(2), vortex removal implies the restoration of chiral symmetry [22][23][24].…”

“…It took until the late '90s until a successful definition was given [16] and the relevance of vortices in the continuum limit was established [17]. The recovery of the string tension from ''vortex-only'' SU(2) gauge configurations (i.e., Z 2 projected from SU(2)) was shown [11][12][13], the finite-temperature deconfinement transition was understood in terms of vortex properties [18][19][20][21] and a connection to D SB was discovered [22][23][24][25].…”

Panel discussion: What don’t we know about confinement?

“…As shown in ref. [36] the quark spectrum develops a gap at zero virtuality when center vortices are removed from the Yang-Mills ensemble.…”

Vacuum structure as seen by overlap fermions

“…2 (left) urges a more detailed study of the lowest eigenmodes, in particular closer to the continuum limit. Case studies [5] show that they might be pinned-down on lowdimension defects of the gauge field (monopoles and vortices, the candidates to create confinement).…”