Construction of the unitary free fermion Segal CFT. (English) Zbl 1406.81085
G. Segal [Lond. Math. Soc. Lect. Note Ser. 308, 421–577 (2004; Zbl 1372.81138)] proposed an abstract definition of conformal field theory as a projective monoidal functor \(E\) defined on a bordism category of Riemann surfaces. The topological version of this notion has been greatly developed in recent years, but examples of CFTs in Segal’s sense remain scarce. The paper under review provides a rigorous construction of the free fermion theory as a (spin) Segal CFT. The domain bordism category is carefully set up and the construction of the functor \(E\) is given in detail, using as main tool the Cauchy transform for Riemann surfaces.
Finally, in order to justify the given construction, it is verified that by evaluating the CFT on suitable pairs of pants, one recovers the free fermion vertex operator algebra.
Finally, in order to justify the given construction, it is verified that by evaluating the CFT on suitable pairs of pants, one recovers the free fermion vertex operator algebra.
Reviewer: Augusto Stoffel (Greifswald)
MSC:
| 81T40 | Two-dimensional field theories, conformal field theories, etc. in quantum mechanics |
| 53C27 | Spin and Spin\({}^c\) geometry |
| 17B69 | Vertex operators; vertex operator algebras and related structures |
| 19D23 | Symmetric monoidal categories |
Keywords:
conformal field theory; free fermion; spin Riemann surfaces; Cauchy transform; vertex operator algebrasCitations:
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