Unitary QFTs are determined up to unitary isomorphism by closed-manifold partition functions; every reflection-positive partition function comes from a unitary QFT, so spatial wormholes do not break Hilbert-space factorization once the full charged spectrum is included.
Vertex operator algebras, partition functions and Teichm\"{u}ller modular forms
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In the spirit of the geometric approach to two-dimensional conformal field theory, we explicitly associate to every holomorphic vertex operator algebra a section of a power of Hodge line bundle on the moduli space of curves of arbitrary genus - or equivalently a Teichm\"{u}ller modular form in any genus. As a first application, we connect the geometry of the moduli space of curves to the classification program for holomorphic vertex algebras. We then discuss how to use the theory of holomorphic vertex algebras to reach new results about the moduli space of curves. In the last part of the paper we study how the above mentioned forms can be used to reconstruct the vertex algebra.
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Wormholes as red herrings: reflection positivity and the reconstruction of unitary quantum field theories
Unitary QFTs are determined up to unitary isomorphism by closed-manifold partition functions; every reflection-positive partition function comes from a unitary QFT, so spatial wormholes do not break Hilbert-space factorization once the full charged spectrum is included.