Radial Quantization for Conformal Field Theories on the Lattice

TL;DR

This paper explores radial quantization of conformal field theories using a lattice approach, applying it to the 3D Ising model to compute critical exponents.

Contribution

It introduces a lattice-based radial quantization method for conformal field theories and demonstrates its application to the 3D Ising model.

Findings

Successfully mapped Euclidean field theory to a cylindrical manifold.

Computed the critical exponent η for the 3D Ising model.

Validated the approach with numerical results.

Abstract

We consider radial quantization for conformal quantum field theory with a lattice regulator. A Euclidean field theory on $\mathbb R^D$ is mapped to a cylindrical manifold, $\mathbb R\times \mathbb S^{D-1}$, whose length is logarithmic in scale separation. To test the approach, we apply this to the 3D Ising model and compute $\eta$ for the first $Z_2$ odd primary operator.