Lattice QCD at finite temperature and density

Abstract

I review recent lattice results on strongly interacting matter under extreme conditions, with emphasis on the finite-temperature QCD transition at $\hat{I}{¼}_B=0$, 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 $\hat{I}{¼}_B>0$. 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.

24 pages, 10 figures, plenary talk presented at the 42nd International Symposium on Lattice Field Theory (Lattice 2025), 2-8 November 2025, Mumbai, India; version in PoS