Towards a semi-classical description of QCD vacuum around $T_c$

TL;DR

This study investigates the topological structures of the QCD vacuum near the critical temperature using lattice simulations, providing evidence that a semi-classical model involving instanton-dyons accurately describes fermionic zero modes just above the transition.

Contribution

It introduces a novel lattice approach combining overlap and domain wall fermions to identify instanton-dyons and quantifies their interactions and densities near the QCD transition temperature.

Findings

Fermion zero modes are consistent with instanton-dyon structures.

Estimated dyon separation is approximately 0.3 fm.

Semi-classical models effectively describe the QCD vacuum just above T_c.

Abstract

We study the vacuum topology of 2+1 flavor QCD above the chiral crossover transition, at $T \lesssim 1.2~T_c$, on lattices of size $32^3\times 8$. Since overlap fermions have exact chiral symmetry and an index theorem even on a finite lattice, we use them to detect the topological content of gauge fields generated using domain wall fermion discretization for quarks. We further use different periodicity phases along the temporal direction for the valence overlap quarks, which allows us to probe different topological structures present in the gauge field ensembles, through its zero modes. This procedure provides strong evidences that fermion zero-modes can be quantitatively understood to arise due to different species of instanton-dyons. We estimate their relative abundances from the Dirac-eigenvalue density and resolve the so called "topological clusters" via multi-parameter fits to their density, providing therefore an understanding of the interactions between instanton-dyons. The typical separation between dyons we obtain, is $\sim 0.3$ fm. Surprisingly, it emerges out from this study that a semi-classical description of the fermionic zero modes in the QCD vacuum is quite accurate just above $T_c$.