Bootstrapping the Abelian lattice gauge theories - INSPIRE

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Bootstrapping the Abelian lattice gauge theories

Zhijin Li
(
- Southeast U., Nanjing
)
,
Shutong Zhou
(
- Nanjing U.
)

Apr 25, 2024

40 pages

Published in:

JHEP 08 (2024) 154

Published: Aug 20, 2024

e-Print:

2404.17071 [hep-th]

DOI:

10.1007/JHEP08(2024)154

View in:

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Abstract: (Springer)

We study the ℤ

_{2}

and U(1) Abelian lattice gauge theories using a bootstrap method, in which the loop equations and positivity conditions are employed for Wilson loops with lengths L ⩽ L

_{max}

to derive two-sided bounds on the Wilson loop averages. We address a fundamental question that whether the constraints from loop equations and positivity are strong enough to solve lattice gauge theories. We answer this question by bootstrapping the 2D U(1) lattice gauge theory. We show that with sufficiently large L

_{max}

= 60, the two-sided bounds provide estimates for the plaquette averages with precision near 10

^{−8}

or even higher, suggesting the bootstrap constraints are sufficient to numerically pin down this theory. We compute the bootstrap bounds on the plaquette averages in the 3D ℤ

_{2}

and U(1) lattice gauge theories with L

_{max}

= 16. In the regions with weak or strong coupling, the two-sided bootstrap bounds converge quickly and coincide with the perturbative results to high precision. The bootstrap bounds are well consistent with the Monte Carlo results in the nonperturbative region. We observe interesting connections between the bounds generated by the bootstrap computations and the Griffiths’ inequalities. We present results towards bootstrapping the string tension and glueball mass in Abelian lattice gauge theories.

Note:

40 pages, 6 figures; v2: typos corrected, refs added, more related data

Lattice Quantum Field Theory
Wilson, ’t Hooft and Polyakov loops
Confinement
Nonperturbative Effects
glueball: mass
lattice field theory
bootstrap
abelian
U(1)
Wilson loop

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