The Operator Product Expansion for Radial Lattice Quantization of 3D $\phi^4$ Theory

TL;DR

This paper applies radial lattice quantization and the Quantum Finite Elements method to 3D $^4$ theory, accurately computing critical exponents and OPE coefficients of the 3D Ising CFT.

Contribution

It introduces a novel radial quantization approach using simplicial lattices and Quantum Finite Elements to study 3D critical $^4$ theory and extract conformal data.

Findings

Accurate determination of $elta_\u03b5$ and $elta_T$

Precise ratios of OPE coefficients $f_{  $ and $f_{  T}$

Validation of radial quantization as a powerful method for CFT analysis

Abstract

At its critical point, the three-dimensional lattice Ising model is described by a conformal field theory (CFT), the 3d Ising CFT. Instead of carrying out simulations on Euclidean lattices, we use the Quantum Finite Elements method to implement radially quantized critical $\phi^4$ theory on simplicial lattices approaching $\mathbb{R} \times S^2$. Computing the four-point function of identical scalars, we demonstrate the power of radial quantization by the accurate determination of the scaling dimensions $\Delta_{\epsilon}$ and $\Delta_{T}$ as well as ratios of the operator product expansion (OPE) coefficients $f_{\sigma \sigma \epsilon}$ and $f_{\sigma \sigma T}$ of the first spin-0 and spin-2 primary operators $\epsilon$ and $T$ of the 3d Ising CFT.