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  The holomorphic bosonic string

Gwilliam, O., & Williams, B. (2018). The holomorphic bosonic string. In Topology and quantum theory in interaction (pp. 213-258). Providence: American Mathematical Society.

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arXiv:1711.05823.pdf (Preprint), 452KB
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https://doi.org/10.1090/conm/718/14481 (Publisher version)
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 Creators:
Gwilliam, Owen1, Author           
Williams, Brian, Author
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1Max Planck Institute for Mathematics, Max Planck Society, ou_3029201              

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Free keywords: Mathematics, Mathematical Physics, High Energy Physics - Theory, Quantum Algebra
 Abstract: We describe and analyze a holomorphic version of the bosonic string in the formalism of quantum field theory developed by Costello and collaborators, which provides a powerful combination of renormalization theory and the Batalin-Vilkovisky formalism. Our focus here is on the case in which the target space-time is a vector space. We identify the critical dimension as an obstruction to satisfying the quantum master equation, and when the
obstruction vanishes, we construct a one-loop exact quantization. Moreover, we show how the factorization algebra of observables recovers the BRST cohomology of the string and use this perspective to give a new construction of its Gerstenhaber structure. Finally, we show how the factorization homology along closed manifolds encodes the determinant line bundle over the moduli
space of Riemann surfaces. An auxiliary goal of this paper is to give an exposition of this QFT formalism with the holomorphic bosonic string theory as the running example.

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Language(s): eng - English
 Dates: 2018
 Publication Status: Issued
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Title: Topological and Geometric Methods in Quantum Field Theory
Place of Event: Montana State University, Bozeman, Montana
Start-/End Date: 2017-07-31 - 2017-08-04

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Title: Topology and quantum theory in interaction
  Subtitle : NSF-CBMS Regional Conference in the Mathematical Sciences Topological and Geometric Methods in QFT, July 31-August 4, 2017, Montana State University, Bozeman, Montana
Source Genre: Proceedings
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Publ. Info: Providence : American Mathematical Society
Pages: xi, 258 Volume / Issue: - Sequence Number: - Start / End Page: 213 - 258 Identifier: ISBN: 978-1-4704-4243-9
DOI: 10.1090/conm/718

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Title: Contemporary mathematics
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Pages: - Volume / Issue: 718 Sequence Number: - Start / End Page: - Identifier: -