×

Wilson loops in finite abelian lattice gauge theories. (English. French summary) Zbl 1513.81102

Summary: We consider lattice gauge theories on \(\mathbb{Z}^4\) with Wilson action and structure group \(\mathbb{Z}_n\). We compute the expectation of Wilson loop observables to leading order in the weak coupling regime, extending and refining a recent result of Chatterjee. Our proofs use neither duality relations nor cluster expansion techniques.

MSC:

81T13 Yang-Mills and other gauge theories in quantum field theory
81T25 Quantum field theory on lattices
PDFBibTeX XMLCite
Full Text: DOI arXiv Link

References:

[1] C. Borgs. Translation symmetry breaking in four dimensional lattice gauge theories. Comm. Math. Phys. 96 (1984) 251-284.
[2] S. Cao. Wilson loop expectations in lattice gauge theories with finite gauge groups. Comm. Math. Phys. 380 (2020) 1439-1505. · Zbl 1483.81114 · doi:10.1007/s00220-020-03912-z
[3] S. Chatterjee. Wilson loops in Ising lattice gauge theory. Comm. Math. Phys. 377 (2020) 307-340. · Zbl 1441.81122 · doi:10.1007/s00220-020-03738-9
[4] J. Fröhlich and T. Spencer. Massless phases and symmetry restoration in Abelian gauge theories and spin systems. Comm. Math. Phys. 83 (1982) 411-454.
[5] C. Gattringer and C. Lang. Quantum Chromodynamics on the Lattice: An Introductory Presentation. Lect. Notes Phys. 788. Springer, Berlin, 2010. · doi:10.1007/978-3-642-01850-3
[6] J. Ginibre. General formulation of Griffiths’ inequalities. Comm. Math. Phys. 16 (1970) 310-328.
[7] K. Wilson. Confinement of quarks. Phys. Rev. D 10 (1974) 2445-2459.
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.