Gauge loop-string-hadron formulation on general graphs and applications to fully gauge fixed Hamiltonian lattice gauge theory

Journal Article · Wed Jan 01 00:00:00 EST 2025 · Journal of High Energy Physics (JHEP)

DOI:https://doi.org/10.1007/jhep12(2025)060· OSTI ID:3012840

Burbano, Ivan M; Bauer, Christian W

We develop a gauge invariant, Loop-String-Hadron (LSH) based representation of SU(2) Yang-Mills theory defined on a general graph consisting of vertices and half-links. Inspired by weak coupling studies, we apply this technique to maximal tree gauge fixing. This allows us to develop a fully gauge-fixed representation of the theory in terms of LSH quantum numbers. We explicitly show how the quantum numbers in this formulation directly relate to the variables in the magnetic description. In doing so, we will also explain in detail how the Kogut-Susskind formulation, prepotentials, and point splitting work for general graphs. In the appendix of this work, we provide a self-contained exposition of the mathematical details of Hamiltonian pure gauge theories defined on general graphs.

• Research Organization: Lawrence Berkeley National Laboratory (LBNL), Berkeley, CA (United States)
• Sponsoring Organization: US Department of Energy; USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
• Grant/Contract Number: AC02-05CH11231
• OSTI ID: 3012840
• Journal Information: Journal of High Energy Physics (JHEP), Journal Name: Journal of High Energy Physics (JHEP) Journal Issue: 12 Vol. 2025
• Country of Publication: United States
• Language: English