Year: 2023
Type: article
Abstract: We demonstrate that the Ising model on a general triangular graph with three distinct couplings ${K}_{1}$, ${K}_{2}$, and ${K}_{3}$ corresponds to an affine transformed conformal field theory (CFT). Full conformal invariance of the $c=1/2$ minimal CFT is restored by introducing a metric on the lattice through the map $\mathrm{sinh}(2{K}_{i})={\ensuremath{\ell}}_{i}^{*}/{\ensuremath{\ell}}_{i}$ which relates critical couplings to the ratio of the dual hexagonal and triangular edge lengths. Applied to a 2D toroidal lattice, this provides an exact lattice formulation in the continuum limit to the Ising CFT as a function of the modular parameter. This example can be viewed as a quantum generalization of the finite element method applied to the strong coupling CFT at a Wilson-Fisher IR fixed point and suggests a new approach to conformal field theory on curved manifolds based on a synthesis of simplicial geometry and projective geometry on the tangent planes.
Authors: Richard C. Brower, Evan K. Owen
Institution: Boston University
Language: English
Subfield: Nuclear and High Energy Physics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: hybrid
OpenAlex ID: W4385156316