Algebraic Supersymmetry: A case study

Abstract

The treatment of supersymmetry is known to cause difficulties in the C*-algebraic framework of relativistic quantum field theory; several no-go theorems indicate that super-derivations and super-KMS functionals must be quite singular objects in a C*-algebraic setting. In order to clarify the situation, a simple supersymmetric chiral field theory of a free Fermi and Bose field defined on $\mathbb{R}$ is analyzed. It is shown that a meaningful C*-version of this model can be based on the tensor product of a CAR-algebra and a novel version of a CCR-algebra, the "resolvent algebra". The elements of this resolvent algebra serve as mollifiers for the super-derivation. Within this model, unbounded (yet locally bounded) graded KMS-functionals are constructed and proven to be supersymmetric. From these KMS-functionals, Chern characters are obtained by generalizing formulae of Kastler and of Jaffe, Lesniewski and Osterwalder. The characters are used to define cyclic cocycles in the sense of Connes' noncommutative geometry which are "locally entire".

55 pages. Final version (to appear in Commun. Math. Phys)

References in corpus (3)

• Towards a Relativistic KMS Condition
• Notes for a Quantum Index Theorem
• Spontaneous Collapse of Supersymmetry

Cited by in corpus (11)

• Spectral triples and the super-Virasoro algebra
• Modular Theory, Non-Commutative Geometry and Quantum Gravity
• The resolvent algebra for oscillating lattice systems: Dynamics, ground and equilibrium states
• Lie Algebras of Derivations and Resolvent Algebras
• Noncompact uniform universal approximation
• Supergeometry in locally covariant quantum field theory
• The K-homology of nets of C*-algebras
• Trapped bosons, thermodynamic limit and condensation: a study in the framework of resolvent algebras
• Super-KMS functionals for graded-local conformal nets
• Local-entire cyclic cocycles for graded quantum field nets
• From Operator Algebras to Superconformal Field Theory