# The 39th International Symposium on Lattice Field Theory (Lattice 2022)

Aug 8 – 13, 2022
Hörsaalzentrum Poppelsdorf
Europe/Berlin timezone

## Numerical studies on the finite-temperature CP restoration in 4D SU($N$) gauge theory at $\theta=\pi$

Aug 8, 2022, 5:10 PM
20m
CP1-HSZ/1st-1.001 - HS5 (CP1-HSZ)

### CP1-HSZ/1st-1.001 - HS5

#### CP1-HSZ

50
Oral Presentation Theoretical Developments and Applications beyond Particle Physics

### Speaker

Dr Akira Matsumoto (RIKEN iTHEMS)

### Description

Recent studies on the 't Hooft anomaly matching condition have suggested
a nontrivial phase structure in 4D SU($N$) gauge theory at $\theta=\pi$.
In the large-$N$ limit, it has been found that CP symmetry at $\theta=\pi$ is broken
in the confined phase, while it restores in the deconfined phase,
which is indeed one of the possible scenarios.
However, at small $N$, one may find other situations that are consistent
with the consequence of the anomaly matching condition.
Here we investigate this issue for $N=2$ by direct lattice calculations.
The crucial point to note is that the CP restoration can be probed
by the sudden change of the tail of the topological charge distribution at $\theta=0$,
which can be seen by simulating the theory at imaginary $\theta$ without the sign problem.
Our results suggest that the CP restoration at $\theta=\pi$ occurs at temperature
higher than the deconfining temperature unlike the situation in the large-$N$ limit.

### Primary author

Dr Akira Matsumoto (RIKEN iTHEMS)

### Co-authors

Dr Kohta Hatakeyama (KEK) Dr Mitsuaki Hirasawa (Istituto Nazionale di Fisica Nucleare (INFN)) Prof. Masazumi Honda (YITP) Prof. Jun Nishimura (KEK) Mr Atis Yosprakob (SOKENDAI)