SIMIS Seminar on Field Theory and String Theory: Bootstrapping the Abelian Lattice Gauge Theories

Speaker: Zhijin Li (Southeast University)

Abstract: In this talk, I will introduce a recent bootstrap study of the Z2 and U(1) Abelian lattice gauge theories, for which the loop equations and positivity conditions are employed for Wilson loops with lengths L ⩽ Lmax to derive two-sided bounds on the Wilson loop averages. I will address a fundamental question that whether the constraints from loop equations and positivity are strong enough to solve lattice gauge theories. This question will be answered by bootstrapping the 2D U(1) lattice gauge theory. I will show that with sufficiently large Lmax = 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. The bootstrap bounds on the plaquette averages in the 3D Z2 and U(1) lattice gauge theories are computed up to Lmax = 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, and there are interesting connections between the bounds generated by the bootstrap computations and the Griffiths’ inequalities. I will present results towards bootstrapping the string tension and glueball mass in Abelian lattice gauge theories and discuss future work for this fascinating problem.

Time: 16:00 ~ 17:00, Thu., May 30, 2024

Location: Floor 6, Innovation Center Building 3, Weicheng Road 62, Yangpu District, Shanghai, China

Zoom Meeting No.: 423 317 8953
Password: SIMIS

Organizer: Sen Hu, Andrey Losev, Bong Lian, Wen-Jie Ma, Hao Zou

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