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

Abstract

Abstract:We introduce topological non-trivial colorful regions around intersection points of two perpendicular vortex pairs and investigate their influence on topological charge density and eigenmodes of the Dirac operator. With increasing distance between the vortices the eigenvalues of the lowest modes decrease. We show that the maxima and minima of the chiral densities of the low modes follow mainly the distributions of the topological charge densities. The topological non-trivial color structures lead in some low modes to distinct peaks in the chiral densities. The other low modes reflect the topological charge densities of the intersection points.

Fractional topological charges and the lowest Dirac modes

“…the continuum while on the lattice the electric field of the colorful region is only observed. In the Q ¼ 0.5 configuration, by substituting the colorful region within the circle of radius R around the point (x 1 , z 1 ), the orientation of the electric field within the circle corresponding to the unicolor vortex becomes opposite orientation due to the insertion of a circular monopole line around the intersection point [37]. Therefore, combining the electric field of circular monopole line of the xy-vortices and the magnetic field of the zt-vortices contributes Q ¼ −0.5.…”

“…Lattice simulations and infrared models have indicated that the random fluctuations of the number of center vortices which are quantized magnetic fluxes in terms of the nontrivial center elements linked to the Wilson loop leads to quark confinement [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20]. In addition, lattice simulations have shown that center vortices are also responsible for topological charge and SCSB [21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37][38]. The vortex intersections could contribute to the topological charge density [14].…”

Branching of center vortices in SU(3) lattice gauge theory

“…Center vortices also seem to carry the non-trivial topological content of gauge fields: the Pontryagin index can be understood as self-intersection number of center vortex sheets in four Euclidean dimensions [4,5] or in terms of the writhing number of their 3-dimensional projection which are loops [5]. For the colour group SU(2), attempts to restore the structure of the underlying (fat) vortices suggest that the topological charge also receives contributions from the colour structure of self-intersection regions of such fat vortices [6,7]. Removing the center vortex content of the gauge fields makes the field configuration topological trivial and simultaneously restores chiral symmetry.…”

Combining the color structures and intersection points of thick center vortices and low-lying Dirac modes

“…Numerical simulations have indicated that the center vortices can account for the phenomena of the color confinement [1][2][3][4][5][6][7][8][9] and spontaneous chiral symmetry breaking [10][11][12][13][14]. Center vortices can contribute to the topological charge through intersection and writhing points [14][15][16][17][18][19][20][21][22][23][24] and their color structure [22,[24][25][26][27][28]. We have studied colorful plane vortices in Refs.…”

“…We have studied colorful plane vortices in Refs. [22,24]. According to the Atiyah-Singer index theorem [29][30][31][32], the zero modes of the Dirac operator are related to the topological charges.…”