The large-$N$ limit of the topological susceptibility of $\mathrm{SU}(N)$ Yang-Mills theories via Parallel Tempering on Boundary Conditions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866911354582990848 |
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| author | Bonanno, Claudio |
| author_facet | Bonanno, Claudio |
| contents | I present a large-$N$ determination of the topological susceptibility $χ$ of $\mathrm{SU}(N)$ Yang--Mills theories using non-perturbative numerical Monte Carlo simulations of the lattice-discretized theory for $3\le N \le 6$, 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2510_08006 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | The large-$N$ limit of the topological susceptibility of $\mathrm{SU}(N)$ Yang-Mills theories via Parallel Tempering on Boundary Conditions Bonanno, Claudio High Energy Physics - Lattice High Energy Physics - Phenomenology High Energy Physics - Theory I present a large-$N$ determination of the topological susceptibility $χ$ of $\mathrm{SU}(N)$ Yang--Mills theories using non-perturbative numerical Monte Carlo simulations of the lattice-discretized theory for $3\le N \le 6$, 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. |
| title | The large-$N$ limit of the topological susceptibility of $\mathrm{SU}(N)$ Yang-Mills theories via Parallel Tempering on Boundary Conditions |
| topic | High Energy Physics - Lattice High Energy Physics - Phenomenology High Energy Physics - Theory |
| url | https://arxiv.org/abs/2510.08006 |