Dual quark condensate and dressed Polyakov loops

Abstract

We construct a new order parameter for finite temperature QCD by considering the quark condensate for U(1)-valued temporal boundary conditions for the fermions. Fourier transformation with respect to the boundary condition defines the dual condensate. This quantity corresponds to an equivalence class of Polyakov loops, thereby being an order parameter for the center symmetry. We explore the duality relation between the quark condensate and these dressed Polyakov loops numerically, using quenched lattice QCD configurations below and above the QCD phase transition. It is demonstrated that the Dirac spectrum responds differently to changing the boundary condition, in a manner that reproduces the expected Polyakov loop pattern. We find the dressed Polyakov loops to be dominated by the lowest Dirac modes, in contrast to thin Polyakov loops investigated earlier.

Figures (3)

• Figure 1: The integrand $I(\varphi) = V^{-1} \sum_i \langle (m + \lambda^{(i)}_\varphi)^{-1} \rangle_G$ of (\ref{['spectralsum']}) in lattice units for two values of $am$. The data are from 20 gauge configurations on $12^3 \times 6$ lattices below ($T$ = 255 MeV, $a$ = 0.129 fm) and above $T_c$ ($T$ = 337 MeV, $a$ = 0.098 fm).
• Figure 2: The dressed Polyakov loop at $m = 100$ MeV in units of GeV$^3$ as a function of the temperature $T$ in MeV.
• Figure 3: The upper plots show the (normalized) individual contributions $|C(|\lambda|)/\widetilde{\Sigma}_1|$ to (\ref{['spectralsum']}) versus $|\lambda|$ for two values of $m$, while the lower plots are for the normalized accumulated contributions $|A(|\lambda|)/\widetilde{\Sigma}_1|$ as a function of $|\lambda|$. The data are from the same ensembles already used in Fig. 1.