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Bootstrap for Finite N Lattice Yang-Mills Theory

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arxiv 2404.16925 v4 pith:RIXLFMW7 submitted 2024-04-25 hep-th hep-lat

Vladimir Kazakov , Zechuan Zheng This is my paper · ORCID
classification hep-thhep-lat
keywords bootstraplatticefinitetheoryyang-millsagreementapproachcarlo
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abstract

We introduce a comprehensive framework for analyzing finite $N$ lattice Yang-Mills theory and finite $N$ matrix models. Utilizing this framework, we examine the bootstrap approach to SU(2) Lattice Yang-Mills Theory in 2,3 and 4 dimensions. The SU(2) Makeenko-Migdal loop equations on the lattice are linear and closed exclusively on single-trace Wilson loops. This inherent linearity significantly enhances the efficiency of the bootstrap approach due to the convex nature of the problem, permitting the inclusion of Wilson loops up to length 24. The exact upper and lower margins for the free energy per plaquette, derived from our bootstrap method, demonstrate good agreement with Monte Carlo data, achieving precision within $0.1\%$ for the physically relevant range of couplings in both three and four dimensions. Additionally, our bootstrap data provides estimates of the string tension, in qualitative agreement with existing Monte Carlo computations.

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Cited by 5 Pith papers

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

  1. Bootstrapping Euclidean Two-point Correlators

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    A semidefinite programming bootstrap is formulated for Euclidean two-point correlators in quantum mechanics, yielding rigorous bounds and low-lying spectrum extraction in the ungauged one-matrix model.

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  3. Bootstrapping periodic quantum systems

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  4. High-Precision Bootstrap of Multimatrix Quantum Mechanics

    hep-th 2025-07 conditional novelty 6.0 of 10

    Semidefinite bootstrap bounds fix the large-N ground-state energy and ⟨trX²⟩ of bosonic matrix quantum mechanics to up to eight significant digits.

  5. Notes on the Loop Equation in Loop Space

    hep-th 2025-08 conditional novelty 4.0 of 10

    A functional Laplace form of the large-N loop equation, solved with a Gaussian path-integral Green function, reproduces Wilson-loop perturbation theory through order (g²N)², including the three-gluon vertex.

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