Instanton-dyon Ensembles III: Exotic Quark Flavors

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.