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

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arxiv 2205.08883 v2 pith:XCPLZZV3 submitted 2022-05-18 hep-lat

Takaaki Kuwahara , Asato Tsuchiya This is my paper · ORCID
classification hep-lat
keywords gaugetensortheoryactionconfigurationsfieldgroupinitial
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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 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 weak and strong coupling regimes.

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Cited by 3 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Deconfinement from Thermal Tensor Networks: Universal CFT signature in (2+1)-dimensional $\mathbb{Z}_N$ lattice gauge theory

    hep-th 2026-02 conditional novelty 7.0 of 10

    Tensor-network contraction of finite-temperature Z_N gauge theory yields central charges and scaling dimensions consistent with Svetitsky–Yaffe universality for N=2,3,5, including a U(1)-symmetric BKT phase for N=5, a...

  2. Forward-mode automatic differentiation for the tensor renormalization group and its relation to the impurity method

    hep-lat 2026-02 conditional novelty 7.0 of 10

    Forward-mode AD for TRG is derived with (k+1)(k+2)/2 cost scaling, linked to impurity methods, and tested on the 2D/3D Ising model for energy, specific heat, and critical exponents.

  3. Toward tensor renormalization group study of lattice QCD

    hep-lat 2025-01 conditional novelty 3.0 of 10

    Tensor renormalization group methods for multi-flavor and non-Abelian gauge theories are summarized with 2D Z2 and 3D SU(2) and SU(3) proof-of-principle results.

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