2025/03/07 by Richard C. Brower, George Fleming, Brower, Richard C. +5
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Physical sciences #High Energy Physics - Lattice (hep-lat) #Quantum many-body systems
paper · pdf · doi:10.48550/arxiv.2503.05621
openalex publication_date 2025/03/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We review the recent construction \citebrower2024isingmodelmathbbs2 of the 2d Ising model on a triangulated sphere \mathbbS2. Surprisingly, this led to a precise map of the lattice couplings to the target geometry in order to reach the conform field theory (CFT) in the continuum limit. For the integrable 2d Ising CFT, the map was found analytically \citeBrower2023. Here we conjecture how this might be generalized. The discrete geometry is implemented by the piecewise flat triangulation introduced by Regge in 1960 for the Einstein Hilbert action \citeRegge1961GeneralRW. Then following our Ising example, we posit the existence of a smooth map of lattice couplings in affine parameters consistent with quantum correlators. A sequence of theoretical investigations and numerical simulations are recommended to test this conjecture. They begin with non-integrable CFT's -- the 2d ϕ4 theory on \mathbbS2; the 3d Ising model on \mathbbS3 and ℝ × \mathbbS2; QED3 on ℝ × \mathbbS2 as an intermediate step to 4d non-Abelian lattice gauge theory on ℝ × \mathbbS3.