Instanton-dyon Ensembles III: Exotic Quark Flavors

TL;DR

This paper investigates how modifying quark boundary conditions with flavor holonomies affects phase transitions in QCD-like models, revealing significant differences in deconfinement and chiral restoration behaviors compared to standard QCD.

Contribution

It introduces a $Z_{N_c}$-symmetric QCD model with equal flavors and colors, demonstrating how flavor holonomies influence topological zero modes and phase transition nature.

Findings

Deconfinement becomes a strong first-order transition in the symmetric model.

Chiral symmetry remains broken across studied densities in the symmetric model.

Results align with recent lattice simulation observations.

Abstract

"Exotic quarks" in the title refers to a modification of quark periodicity condition on the thermal circle by introduction of some phases -- known also as "flavor holonomies" -- different quark flavors. These phases provide a valuable tool, to be used for better understanding of deconfinement and chiral restoration phase transitions: by changing them one can dramatically modify both phase transitions. In the language of instanton constituents -- instanton-dyons or monopoles -- it has a very direct explanation: the interplay of flavor and color holonomies can switch topological zero modes between various dyon types. The model we will study in detail, the so called $Z_{N_c}$-symmetric QCD model with equal number of colors and flavors $N_c=N_f=2$ and special arrangement of flavor and color holonomies, ensure "most democratic" setting, in which each quark flavor and each dyon type are in one-to-one correspondence. The usual QCD has the opposite "most exclusive" arrangement: all quarks are antiperiodic and thus all zero modes fall on only one -- twisted or $L$ -- dyon type. As we show by ensemble simulation, deconfinement and chiral restoration phase transitions in these two models are dramatically different. In the usual QCD both are smooth crossovers: but in the case of $Z_2$-symmetric model deconfinement becomes strong first order transition, while chiral symmetry remains broken for all dyon densities studied. These results are in good correspondence with those from recent lattice simulations.