The imaginary-$\theta$ dependence of the SU($N$) spectrum

Abstract

In this talk we will report on a study of the $\theta$-dependence of the string tension and of the mass gap of four-dimensional SU($N$) Yang--Mills theories. The spectrum at $N=3$ and $N=6$ was obtained on the lattice at various imaginary values of the $\theta$-parameter, using Parallel Tempering on Boundary Conditions to avoid topological freezing at fine lattice spacings. The coefficient of the $\mathcal{O}({\theta }^2)$ term in the Taylor expansion of the spectrum around $\theta =0$ could be obtained in the continuum limit for $N=3$, and on two fairly fine lattices for $N=6$.

Comments: 15 pages, 3 figures. Contribution to Proceedings of the 41st International Symposium on Lattice Field Theory (Lattice 2024), July 28th - August 3rd, 2024, University of Liverpool, UK