Lattice QCD at finite temperature and density

TL;DR

This review summarizes recent lattice QCD findings on the behavior of strongly interacting matter under extreme conditions, including phase transitions, anomalies, and effects of external fields, highlighting methodological advances.

Contribution

It provides a comprehensive overview of recent progress in lattice QCD studies of finite-temperature and density effects, including new insights into the QCD phase diagram and computational techniques.

Findings

Finite-temperature QCD transition at zero chemical potential analyzed.

Constraints on the QCD phase boundary and critical endpoint discussed.

Advances in lattice methods for external conditions like magnetic fields and rotation highlighted.

Abstract

I review recent lattice results on strongly interacting matter under extreme conditions, with emphasis on the finite-temperature QCD transition at $\mu_B=0$, its approach toward the chiral limit and the fate of the $U_A(1)$ anomaly, as well as recent constraints on the QCD phase boundary and the possible critical endpoint at $\mu_B>0$. I also discuss selected advances in lattice methods and in QCD thermodynamics under external conditions, in particular strong magnetic fields, isospin chemical potential, rotation, acceleration, and quark spin polarization.