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Scale setting of SU(N) Yang–Mills theory, topology and large-N volume independence

Claudio Bonanno1,*, Jorge Luis Dasilva Golán2,†, Margarita García Pérez1,‡, Massimo D’Elia3,§, and Andrea Giorgieri3,∥

  • *Contact author: claudio.bonanno@csic.es
  • †Contact author: jgolandas@bnl.gov
  • ‡Contact author: margarita.garcia@csic.es
  • §Contact author: massimo.delia@unipi.it
  • ∥Contact author: andrea.giorgieri@phd.unipi.it
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Phys. Rev. D 113, 074501 – Published 2 April, 2026

DOI: https://doi.org/10.1103/qtqt-hdpz

Abstract

We set the scale of SU(N) Yang-Mills theories for N=3, 5, 8 and in the large-N limit via gradient flow, as a first step towards the computation of the large-N Λ-parameter using step scaling. We adopt twisted boundary conditions to achieve large-N volume reduction and the Parallel Tempering on Boundary Conditions algorithm to tame topological freezing. This setup allows accurate determinations of the gradient-flow scales down to lattice spacings as fine as ∼0.025  fm for all the explored values of N, a regime that has never been reached with ergodic algorithms. Moreover, we are able to precisely estimate the finite-size systematics related to topological freezing, and to show the suppression of finite-volume effects expected by virtue of large-N twisted volume reduction.

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Phys. Rev. D 113, 074501– Published 2 April, 2026
  • Received 18 November 2025
  • Accepted 3 March 2026
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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