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Bootstrap for Lattice Yang-Mills theory

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arxiv 2203.11360 v6 pith:2A4NEHGD submitted 2022-03-21 hep-th hep-lat

Vladimir Kazakov , Zechuan Zheng This is my paper · ORCID
classification hep-thhep-lat
keywords bootstraptheorydatalatticeapproachboundcouplingdimensions
verification ladder T0 review T1 audit T2 compute T3 formal
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abstract

We study the $SU(\infty)$ lattice Yang-Mills theory at the dimensions $D=2,3,4$ via the numerical bootstrap method. It combines the Makeenko-Migdal loop equations, with a cut-off $L_{\mathrm{max}}$ on the maximal length of loops, and positivity conditions on certain matrices of Wilson loops. Our algorithm is inspired by the pioneering paper of P. Anderson and M. Kruczenski but it is significantly more efficient, as it takes into account the symmetries of the lattice theory and uses the relaxation procedure in line with our previous work on matrix bootstrap. We thus obtain rigorous upper and lower bounds on the plaquette average at various couplings and dimensions. For $D=4$, the lower bound data appear to be close to the MC data in the strong coupling phase and the upper bound data in the weak coupling phase reproduce well the 3-loop perturbation theory. Our results suggest that this bootstrap approach can provide a tangible alternative to the, so far uncontested, Monte Carlo approach.

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Cited by 6 Pith papers

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