Fermilab Theory Seminars

The Lattice Ising Model on $S^2$ - The Affine Conjecture

by Richard C. Brower (Boston University)

US/Central
Curia II

Curia II

Description

A formulation of the 2-dimensional Ising model on a triangulated Riemann sphere is presented that converges to the exact conformal field theory (CFT) in the continuum limit. The solution is based on reconciling Regge's simplicial geometry for the Einstein Hilbert action with an Affine map to quantum correlators on the tangent plane. It is conjectured that the fundamental Affine map may in principle be extended to general lattice  quantum field theories  in higher dimensions opening up the use of radial quantization for conformal or near conformal theories on $R x S^{d-1}$ and its $AdS^{d+1}$ dual. A rough road map is suggested for further test in higher  dimension including the long range goal of applications to 4d BSM gauge field theories.