{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/topological-charge-using-cooling-and-the","title":"Topological charge using cooling and the gradient flow","arxiv_id":"1509.04259","date":"2015-09-14","proceeding":null,"authors":["Constantia Alexandrou","Andreas Athenodorou","Karl Jansen"],"abstract":"The equivalence of cooling to the gradient flow when the cooling step $n_c$ and the continuous flow step of gradient flow $\\tau$ are matched is generalized to gauge actions that include rectangular terms. By expanding the link variables up to subleading terms in perturbation theory, we relate $n_c$ and $\\tau$ and show that the results for the topological charge become equivalent when rescaling $\\tau \\simeq n_c/({3-15 c_1})$ where $c_1$ is the Symanzik coefficient multiplying the rectangular term. We, subsequently, apply cooling and the gradient flow using the Wilson, the Symanzik tree-level improved and the Iwasaki gauge actions to configurations produced with $N_f=2+1+1$ twisted mass fermions. We compute the topological charge, its distribution and the correlators between cooling and gradient flow at three values of the lattice spacing demonstrating that the perturbative rescaling $\\tau \\simeq n_c/({3-15 c_1})$ leads to equivalent results.","url_abs":"http://arxiv.org/abs/1509.04259v1","url_pdf":"http://arxiv.org/pdf/1509.04259v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"links_only","authors_date_abstract":"arXiv metadata, CC0 1.0 (https://info.arxiv.org/help/license), from the Kaggle arXiv metadata snapshot of 2026-09-12"},"code_links":[{"paper_slug":"topological-charge-using-cooling-and-the","repo_url":"https://github.com/akio-tomiya/Gaugefields.jl","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"none","reach":{"status":"ok","spdx":"MIT"}}],"tasks":[],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}