Rotational KMS states and type I conformal nets

TL;DR

This paper studies KMS states on conformal nets on the circle, proving that for type I nets, extremal KMS states are Gibbs states, with applications to several well-known models.

Contribution

It establishes that extremal KMS states are Gibbs states for type I conformal nets and verifies this for important classes like rational nets and the U(1)-current net.

Findings

Extremal KMS states are Gibbs states in irreducible representations for type I nets.

Several classes of nets, including rational and U(1)-current nets, are shown to be of type I.

All factorial KMS states are Gibbs states in the completely rational case.

Abstract

We consider KMS states on a local conformal net on the unit circle with respect to rotations. We prove that, if the conformal net is of type I, namely if it admits only type I DHR representations, then the extremal KMS states are the Gibbs states in an irreducible representation. Completely rational nets, the U(1)-current net, the Virasoro nets and their finite tensor products are shown to be of type I. In the completely rational case, we also give a direct proof that all factorial KMS states are Gibbs states.