Categories of Lagrangian Correspondences in Super Hilbert Spaces and Fermionic Functorial Field Theory

Abstract

In this paper, we study Lagrangian correspondences between Hilbert spaces. A main focus is the question when the composition of two Lagrangian correspondences is again Lagrangian. Our answer leads in particular to a well-defined composition law in a category of Lagrangian correspondences respecting given polarizations of the Hilbert spaces involved. As an application, we construct a functorial field theory on geometric spin manifolds with values in this category of Lagrangian correspondences, which can be viewed as a formal Wick rotation of the theory associated to a free fermionic particle in a curved spacetime.

References in corpus (3)

• The Classification of Two-Dimensional Extended Topological Field Theories
• Guide to Boundary Value Problems for Dirac-Type Operators
• The Chiral Anomaly of the Free Fermion in Functorial Field Theory