Lattice gradient flows (de-)stabilizing topological sectors

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Hauptverfasser: Tanizaki, Yuya, Tomiya, Akio, Watanabe, Hiromasa
Format: Preprint
Veröffentlicht: 2024
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author Tanizaki, Yuya
Tomiya, Akio
Watanabe, Hiromasa
author_facet Tanizaki, Yuya
Tomiya, Akio
Watanabe, Hiromasa
contents We investigate the stability of topological charge under gradient flow taking the admissibility condition into account. For the $SU(2)$ Wilson gauge theory with $β=2.45$ and $L^4=12^4$, we numerically show that the gradient flows with the Iwasaki and DBW2 gauge actions stabilize the topological sectors significantly, and they have qualitatively different behaviors compared with the Wilson and tree-level Symanzik flows. By considering the classical continuum limit of the flow actions, we discuss that the coefficient of dimension-$6$ operators has to be positive for stabilizing the one-instanton configuration, and the Iwasaki and DBW2 actions satisfy this criterion while the Wilson and Symanzik actions do not. Moreover, we observe that the DBW2 flow stabilizes the topological sectors at the very early stage of the flow ($\hat{t}\approx 0.5$--$1$), suggesting that a further systematic investigation of the DBW2 flow is warranted to confirm its computational efficiency in determining the gauge topology.
format Preprint
id arxiv_https___arxiv_org_abs_2411_14812
institution arXiv
publishDate 2024
record_format arxiv
spellingShingle Lattice gradient flows (de-)stabilizing topological sectors
Tanizaki, Yuya
Tomiya, Akio
Watanabe, Hiromasa
High Energy Physics - Lattice
High Energy Physics - Theory
Nuclear Theory
We investigate the stability of topological charge under gradient flow taking the admissibility condition into account. For the $SU(2)$ Wilson gauge theory with $β=2.45$ and $L^4=12^4$, we numerically show that the gradient flows with the Iwasaki and DBW2 gauge actions stabilize the topological sectors significantly, and they have qualitatively different behaviors compared with the Wilson and tree-level Symanzik flows. By considering the classical continuum limit of the flow actions, we discuss that the coefficient of dimension-$6$ operators has to be positive for stabilizing the one-instanton configuration, and the Iwasaki and DBW2 actions satisfy this criterion while the Wilson and Symanzik actions do not. Moreover, we observe that the DBW2 flow stabilizes the topological sectors at the very early stage of the flow ($\hat{t}\approx 0.5$--$1$), suggesting that a further systematic investigation of the DBW2 flow is warranted to confirm its computational efficiency in determining the gauge topology.
title Lattice gradient flows (de-)stabilizing topological sectors
topic High Energy Physics - Lattice
High Energy Physics - Theory
Nuclear Theory
url https://arxiv.org/abs/2411.14812