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Defects via factorization algebras

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Abstract

We provide a mathematical formulation of the idea of a defect for a field theory, in terms of the factorization algebra of observables and using the BV formalism. Our approach follows a well-known ansatz identifying a defect as a boundary condition along the boundary of a blowup, but it uses recent work of Butson–Yoo and Rabinovich on boundary conditions and their associated factorization algebras to implement the ansatz. We describe how a range of natural examples of defects fits into our framework.

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Acknowledgements

We have benefited from discussions with many people about defects, factorization algebras, and the BV formalism. We would like to thank Iván Burbano, Dylan Butson, Alberto Cattaneo, Kevin Costello, John Francis, Ben Heidenreich, Rune Haugseng, John Huerta, Theo Johnson-Freyd, Pavel Mnev, Eugene Rabinovich, Ingmar Saberi, Pavel Safronov, Claudia Scheimbauer, Michele Schiavina, Christoph Schweigert, Stephan Stolz, Matt Szczesny, Peter Teichner, Ödül Tetik, Alessandro Valentino, Konstantin Wernli, Brian Williams, and Philsang Yoo; undoubtedly more should be listed, as this is a frequent topic of conversation. Pavel Mnev, in particular, suggested some useful literature and history, and Ödül Tetik explained his ideas for pursuing geometric versions of the Ayala–Francis–Tanaka results. The referee gave us helpful feedback that clarified several points and caught several errors; we appreciate their close reading and encouragement. The National Science Foundation supported O.G. through DMS Grants No. 1812049 and 2042052. I.C. thanks the Amherst College Provost and Dean of the Faculty’s Research Fellowship (2021–2022).

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  1. Amherst College, Amherst, USA

    Ivan Contreras

  2. University of Massachusetts, Amherst, USA

    Chris Elliott & Owen Gwilliam

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  1. Ivan Contreras
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  2. Chris Elliott
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Correspondence to Ivan Contreras.

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Contreras, I., Elliott, C. & Gwilliam, O. Defects via factorization algebras. Lett Math Phys 113, 46 (2023). https://doi.org/10.1007/s11005-023-01670-2

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