https://doi.org/10.1140/epjc/s10052-024-13261-z
Regular Article - Theoretical Physics
The 
twisted gradient flow strong coupling without topological freezing
1
Instituto de Física Téorica UAM-CSIC, Universidad Autónoma de Madrid, Calle Nicolás Cabrera 13-15, Cantoblanco, 28049, Madrid, Spain
2
Physics Deparment, Brookhaven National Laboratory, 11973, Upton, NY, USA
3
Dipartimento di Fisica dell’Università di Pisa and INFN Sezione di Pisa, Largo Pontecorvo 3, 56127, Pisa, Italy
Received:
27
May
2024
Accepted:
16
August
2024
Published online:
10
September
2024
We investigate the role of topology on the lattice determination of the strong coupling renormalized via gradient flow. To deal with the topological freezing of standard local algorithms, the definition of the coupling is usually projected onto the zero topological sector. However, it is not obvious that this definition is not biased by the loss of ergodicity. We instead avoid the topological freezing using a novel algorithm, the Parallel Tempering on Boundary Conditions. The comparison with a standard algorithm shows that, even in the case where the latter is severely frozen, one obtains the same projected coupling. Moreover, we show that the two definitions of the coupling, projected and non-projected, lead to the same flow of the renormalization scale. Our results imply that projecting the coupling does not affect the determination of the dynamically-generated scale of the theory 
, as obtained through the step-scaling method.
© The Author(s) 2024
Open Access This article is licensed under a Creative Commons Attribution 4.0 International License, which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. The images or other third party material in this article are included in the article’s Creative Commons licence, unless indicated otherwise in a credit line to the material. If material is not included in the article’s Creative Commons licence and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder. To view a copy of this licence, visit http://creativecommons.org/licenses/by/4.0/.
Funded by SCOAP3.
