Annales Henri Poincaré

, Volume 16, Issue 8, pp 1899–1936 | Cite as

Super-KMS Functionals for Graded-Local Conformal Nets

  • Robin HillierEmail author


Motivated by a few preceding papers and a question of R. Longo, we introduce super-KMS functionals for graded translation-covariant nets over \({\mathbb{R}}\) with superderivations, roughly speaking as a certain supersymmetric modification of classical KMS states on translation-covariant nets over \({\mathbb{R}}\), 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 \({c\ge 3/2}\). Moreover, as a separate result, we classify bounded super-KMS functionals for graded-local conformal nets over S 1 with respect to rotations.


Irreducible Representation Canonical Commutation Relation Cyclic Cocycles Irreducible General Representation Conformal Subnet 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


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Authors and Affiliations

  1. 1.Department of Mathematics and StatisticsLancaster UniversityLancasterUK

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