Instanton-dyon liquid model. V. Twisted light quarks

Abstract

We discuss an extension of the instanton-dyon liquid model that includes twisted light quarks in the fundamental representation with explicit ZN c symmetry for the case with equal number of colors Nc and flavors N f . We map the model on a 3-dimensional quantum effective theory, and analyze it in the mean-field approximation. The effective potential and the vacuum chiral condensates are made explicit for N f = Nc = 2, 3. The low temperature phase is center symmetric but breaks spontaneously flavor symmetry with N f − 1 massless pions. The high temperature phase breaks center symmetry but supports finite and unequal quark condensates.

Circle compactification and ’t Hooft anomaly

“…The same boundary condition is also used for different and various purposes, such as the reduction of finitevolume effect in lattice simulations, definition of new order parameters, etc. [48,[68][69][70][71] 7 . We especially compare the 't Hooft anomaly (4.15) with the lattice simulation about thermodynamic properties of Z N -QCD [60].…”

Recent progress in understanding deconfinement and chiral restoration phase transitions

“…While in [20] the < P > reaches zero smoothly, a la second order transition, the simulations [25] and lattice [35] both see clear jump in its value indicated strong first order transition. The red squares at Fig.6(left) from [25] are comparing the behavior of the mean Polyakov line in Z 2 and ordinary QCD.…”

“…The Z(N c ) QCD has been studied in the mean field framework [20], by statistical simulations [25] and also by lattice simulations [35]. The first two papers consider the N c = N f = 2 version of the theory, while the last one focus on the N c = N f = 3.…”

“…We will focus on a series of papers devoted to high-density phase and mean field approximation [16][17][18][19][20] in section 3, and on the direct numerical simulation of the dyon ensembles [21][22][23][24][25] in section 4.…”

Order Parameters and Color-Flavor Center Symmetry in QCD

“…× (tr Ω n f +h.c.) + (holonomy-independent), (12) up to exponentially small corrections. The e −πT Ln f factor arises from the lowest fermionic Matsubara frequency and our twisted boundary conditions.…”