Toward tensor renormalization group study of three-dimensional non-Abelian gauge theory

Abstract We propose a method to represent the path integral over gauge fields as a tensor network. We introduce a trial action with variational parameters and generate gauge field configurations with the weight defined by the trial action. We construct initial tensors with indices labelling these ga...

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Published inProgress of theoretical and experimental physics Vol. 2022; no. 9
Main Authors Kuwahara, Takaaki, Tsuchiya, Asato
Format Journal Article
LanguageEnglish
Published Oxford Oxford University Press 01.09.2022
Subjects
Approximation
B01
B38
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Summary:Abstract We propose a method to represent the path integral over gauge fields as a tensor network. We introduce a trial action with variational parameters and generate gauge field configurations with the weight defined by the trial action. We construct initial tensors with indices labelling these gauge field configurations. We perform the tensor renormalization group (TRG) with the initial tensors and optimize the variational parameters. As a first step to the TRG study of non-Abelian gauge theory in more than two dimensions, we apply this method to three-dimensional pure SU(2) gauge theory. Our result for the free energy agrees with the analytical results in the weak and strong coupling regimes.
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ISSN:2050-3911
2050-3911
DOI:10.1093/ptep/ptac103