Super-KMS functionals for graded-local conformal nets

TL;DR

This paper introduces super-KMS functionals as supersymmetric modifications of classical KMS states for graded-local conformal nets, providing existence, partial uniqueness, and classification results in specific models.

Contribution

It defines super-KMS functionals for graded-local nets, proves their existence in certain models, and classifies bounded super-KMS functionals over S^1.

Findings

Existence of super-KMS functionals for supersymmetric free fields and super-Virasoro nets.

Partial uniqueness of super-KMS functionals in specific models.

Classification of bounded super-KMS functionals over the circle.

Abstract

Motivated by a few preceding papers and a question of R. Longo, we introduce super-KMS functionals for graded translation-covariant nets over R with superderivations, roughly speaking as a certain supersymmetric modification of classical KMS states on translation-covariant nets over R, fundamental objects in chiral algebraic quantum field theory. Although we are able to make a few statements concerning their general structure, most properties will be studied in the setting of specific graded-local (super-) conformal models. In particular, we provide a constructive existence and partial uniqueness proof of super-KMS functionals for the supersymmetric free field, for certain subnets, and for the super-Virasoro net with central charge c>= 3/2. Moreover, as a separate result, we classify bounded super-KMS functionals for graded-local conformal nets over S^1 with respect to rotations.