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Wilson loops in the abelian lattice Higgs model

Malin P. Forsström, Jonatan Lenells and Fredrik Viklund

Vol. 4 (2023), No. 2, 257–329
DOI: 10.2140/pmp.2023.4.257
Abstract

We consider the lattice Higgs model on 4 in the fixed length limit, with structure group given by n for n 2. We compute the expected value of the Wilson loop observable to leading order when the inverse temperature and hopping parameter are both sufficiently large compared to the length of the loop. The leading order term is expressed in terms of a quantity arising from the related but much simpler n model, which reduces to the usual Ising model when n = 2. As part of the proof, we construct a coupling between the lattice Higgs model and the n model.

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Keywords
lattice gauge theory, abelian lattice Higgs model, Wilson loops
Mathematical Subject Classification
Primary: 70S15, 81T13, 81T25, 82B20
Milestones
Received: 13 July 2021
Revised: 24 August 2022
Accepted: 25 September 2022
Published: 31 May 2023
Authors
Malin P. Forsström
Department of Mathematics
KTH Royal Institute of Technology
Stockholm
Sweden
Jonatan Lenells
Department of Mathematics
KTH Royal Institute of Technology
Stockholm
Sweden
Fredrik Viklund
Department of Mathematics
KTH Royal Institute of Technology
Stockholm
Sweden