Conformal bootstrap for percolation and polymers

TL;DR

This paper applies the conformal bootstrap method to study percolation and self-avoiding polymers in various dimensions, proposing a Virasoro-inspired operator spectrum without a stress tensor to analyze theories with central charge zero.

Contribution

It introduces a novel Virasoro-inspired spectrum for conformal bootstrap analysis of $c=0$ theories, extending to higher dimensions for percolation and polymers.

Findings

Spectrum devoid of stress tensor effectively enforces $c=0$

Results span multiple dimensions for percolation and polymers

Provides new insights into $c=0$ conformal field theories

Abstract

The conformal bootstrap is applied to percolation and dilute self-avoiding polymers, two theories with Virasoro central charge $c=0$ in two dimensions. In both cases we propose a spectrum of operators motivated by Virasoro symmetry which is devoid of a stress energy tensor as an approximate means of enforcing $c=0$. Percolation is treated in $2\leq D \leq 6$ dimensions, and the self-avoiding walk in $2 \leq D \leq 4$.