Non-unitary observables in the 2d critical Ising model

TL;DR

This paper introduces three non-local observables in the 2D critical Ising model and uses conformal field theory to predict their asymptotic behavior, revealing new highest weights from the Kac table.

Contribution

The paper presents novel non-local observables and derives explicit conformal field theory predictions for their asymptotics at criticality.

Findings

Asymptotics described by highest weights h_{pq} from the Kac table

Identifies weights distinct from known unitary representations

Provides explicit formulae for the behavior of these observables

Abstract

We introduce three non-local observables for the two-dimensional Ising model. At criticality, conformal field theory may be used to obtain theoretical predictions for their behavior. These formulae are explicit enough to show that their asymptotics are described by highest weights $h_{pq}$ from the Kac table for c=1/2 distinct from those of the three unitary representations (0, 1/16 and 1/2).