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Twisted Supergravity and Koszul Duality: A Case Study in AdS₃

Costello, Kevin and Paquette, Natalie M. (2021) Twisted Supergravity and Koszul Duality: A Case Study in AdS₃. Communications in Mathematical Physics, 384 (1). pp. 279-339. ISSN 0010-3616. doi:10.1007/s00220-021-04065-3.

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In this note, we study a simplified variant of the familiar holographic duality between supergravity on AdS₃ × S³ × T⁴ and the SCFT (on the moduli space of) the symmetric orbifold theory Sym^N(T⁴) as N→∞. This variant arises conjecturally from a twist proposed by the first author and Si Li. We recover a number of results concerning protected subsectors of the original duality working directly in the twisted bulk theory. Moreover, we identify the symmetry algebra arising in the N→∞ limit of the twisted gravitational theory. We emphasize the role of Koszul duality—a ubiquitous mathematical notion to which we provide a friendly introduction—in field theory and string theory. After illustrating the appearance of Koszul duality in the “toy” example of holomorphic Chern-Simons theory, we describe how (a deformation of) Koszul duality relates bulk and boundary operators in our twisted setup, and explain how one can compute algebra OPEs diagrammatically using this notion. Further details, results, and computations will appear in a companion paper.

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Paquette, Natalie M.0000-0003-2078-7165
Alternate Title:Twisted Supergravity and Koszul Duality: A Case Study in AdS3
Additional Information:© 2021 The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2021. Received 26 January 2020; Accepted 08 March 2021; Published 07 April 2021. N.P. wishes to thank J. Hilburn, T. Dimofte, and P. Yoo for enjoyable conversations about the many faces of Koszul duality, and M. Cheng, S. Kachru, C. Keller, G. Moore and especially N. Benjamin for earlier collaborations and many enlightening discussions on AdS₃. The work of N.P is supported by a Sherman Fairchild Postdoctoral Fellowship. This material is based upon work supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award Number DE-SC0011632. N.P. is grateful to the Perimeter Institute, UC Davis, and the University of Amsterdam for hospitality during various stages of this work. K.C. would like to thank Davide Gaiotto and Si Li for many illuminating collaborations and conversations about twisted supergravity, holography and Koszul duality over the years. The research of K.C. is supported by the Krembil Foundation and the NSERC Discovery program. Research at Perimeter Institute is supported by the Government of Canada through the Department of Innovation, Science and Economic Development and by the Province of Ontario through the Ministry of Research and Innovation.
Group:Walter Burke Institute for Theoretical Physics
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Sherman Fairchild FoundationUNSPECIFIED
Department of Energy (DOE)DE-SC0011632
Krembil FoundationUNSPECIFIED
Natural Sciences and Engineering Research Council of Canada (NSERC)UNSPECIFIED
Department of Innovation, Science and Economic Development (Canada)UNSPECIFIED
Ontario Ministry of Research and InnovationUNSPECIFIED
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Issue or Number:1
Record Number:CaltechAUTHORS:20200601-103149327
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Official Citation:Costello, K., Paquette, N.M. Twisted Supergravity and Koszul Duality: A Case Study in AdS3. Commun. Math. Phys. 384, 279–339 (2021).
Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:103597
Deposited By: Tony Diaz
Deposited On:01 Jun 2020 17:42
Last Modified:06 May 2021 18:12

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