The large-N limit of the topological susceptibility of SU(N) Yang-Mills theories via Parallel Tempering on Boundary Conditions

A bstract I present a large- N determination of the topological susceptibility χ of SU( N ) Yang-Mills theories using non-perturbative numerical Monte Carlo simulations of the lattice-discretized theory for 3 ≤ N ≤ 6, and adopting the Parallel Tempering on Boundary Conditions (PTBC) algorithm to bypass topological freezing for N > 3. Thanks to this algorithm I am able to explore a uniform range of lattice spacings across all values of N , and to precisely determine χ for finer lattice spacings compared to previous studies with periodic or open boundary conditions. By taking the continuum limit at fixed smoothing radius in physical units, I am also able to show the independence of the continuum limit of χ from this choice. I conclude providing a comprehensive comparison of my new PTBC results with previous determinations of the topological susceptibility in the literature, both at finite N and in the large- N limit.