Construction of the Unitary Free Fermion Segal CFT

@article{Tener2016ConstructionOT,
  title={Construction of the Unitary Free Fermion Segal CFT},
  author={James E. Tener},
  journal={Communications in Mathematical Physics},
  year={2016},
  volume={355},
  pages={463-518}
}
  • James E. Tener
  • Published 6 August 2016
  • Mathematics
  • Communications in Mathematical Physics
In this article, we provide a detailed construction and analysis of the mathematical conformal field theory of the free fermion, defined in the sense of Graeme Segal. We verify directly that the operators assigned to disks with two disks removed correspond to vertex operators, and use this to deduce analytic properties of the vertex operators. One of the main tools used in the construction is the Cauchy transform for Riemann surfaces, for which we establish several properties analogous to those… 
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References

SHOWING 1-10 OF 33 REFERENCES
Construction of the unitary free fermion Segal conformal field theory
Author(s): Tener, James Elliot | Advisor(s): Jones, Vaughan F. R. | Abstract: This thesis is primarily concerned with the construction and analysis of free fermion Segal CFTs in arbitrary genus, with
Riemann surfaces with boundaries and the theory of vertex operator algebras
The connection between Riemann surfaces with boundaries and the theory of vertex operator algebras is discussed in the framework of conformal field theories defined by Kontsevich and Segal and in the
Operator algebras and conformal field theory III. Fusion of positive energy representations of LSU(N) using bounded operators
I. Positive energy representations of LSU(N) 477 II. Local loop groups and their von Neumann algebras 491 III. The basic ordinary di€erential equation 505 IV. Vector and dual vector primary ®elds 513
Geometry and Quantum Field Theory (PDF)
Geometry and Quantum Field Theory, designed for mathematicians, is a rigorous introduction to perturbative quantum field theory, using the language of functional integrals. It covers the basics of
Unitary representations of some infinite dimensional groups
We construct projective unitary representations of (a) Map(S1;G), the group of smooth maps from the circle into a compact Lie groupG, and (b) the group of diffeomorphisms of the circle. We show that
From Vertex Operator Algebras to Conformal Nets and Back
We consider unitary simple vertex operator algebras whose vertex operators satisfy certain energy bounds and a strong form of locality and call them strongly local. We present a general procedure
The Cauchy Transform, Potential Theory and Conformal Mapping
Introduction. The Improved Cauchy Integral Formula. The Cauchy Transform. The Hardy Space, the Szego Projection, and the Kerzman-Stein Formula. The Kerzman-Stein Operator and Kernel. The Classical
The Dirac Equation
Ever since its invention in 1929 the Dirac equation has played a fundamental role in various areas of modern physics and mathematics. Its applications are so widespread that a description of all
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