Speaker
Description
Placing lattice field theories on curved spacetimes requires more than a choice of triangulation: the UV couplings must encode the real-space geometry seen by long-distance observables. Motivated by Brower and Owen's solution for the 2D Ising model on a latticized two-sphere [arXiv:2407.00459], the affine-plane Ising construction [arXiv:2209.15546] and the affine conjecture [arXiv:2503.05621], we develop a numerical method for determining this coupling-geometry map for non-integrable models. In a 2D Ising testbed, we construct the map empirically by matching reweighted critical correlators between boundary-deformed and coupling-deformed lattices. The recovered map agrees with the known affine geometry structure within current uncertainties, supporting the method as a bridge to non-integrable curved-space lattice field theory. The target application is the critical 3D Ising model on R x S2, where radial quantization would allow direct comparison of conformal data with conformal bootstrap and fuzzy-sphere calculations. Future applications include gauge theories on R x S2, including QED3 [arXiv:2510.03085], and four-dimensional gauge theories on R x S3.