Polchinski ERG equation and 2D scalar field theory

TL;DR

This paper uses the Polchinski ERG equation to study 2D scalar field theories, providing evidence it captures non-perturbative fixed points and computing critical exponents consistent with conformal field theories.

Contribution

It demonstrates the applicability of the Polchinski ERG equation to 2D scalar theories and identifies how specific regulators improve the fit to conformal data.

Findings

Polchinski ERG captures fixed points related to 2D conformal theories.

Computed anomalous dimension η and critical exponent ν.

Regulating functions influence the accuracy of conformal field theory fits.

Abstract

We investigate a $Z_2$-symmetric scalar field theory in two dimensions using the Polchinski exact renormalization group equation expanded to second order in the derivative expansion. We find preliminary evidence that the Polchinski equation is able to describe the non-perturbative infinite set of fixed points in the theory space, corresponding to the minimal unitary series of 2D conformal field theories. We compute the anomalous scaling dimension $\eta$ and the correlation length critical exponent $\nu$ showing that an accurate fit to conformal field theory selects particular regulating functions.