Non-Semisimple TQFT's and BPS -Series

We propose and, in some cases, prove a precise relation between 3-manifold invariants associated with quantum groups at roots of unity and at generic . Both types of invariants are labeled by extra data, which plays an important role in the proposed relation. Bridging the two sides - which until rec...

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Опубліковано в: :Symmetry, Integrability and Geometry: Methods and Applications
Дата:2023
Автори: Costantino, Francesco, Gukov, Sergei, Putrov, Pavel
Формат: Стаття
Мова:Англійська
Опубліковано: Інститут математики НАН України 2023
Онлайн доступ:https://nasplib.isofts.kiev.ua/handle/123456789/211874
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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Non-Semisimple TQFT's and BPS -Series. Francesco Costantino, Sergei Gukov and Pavel Putrov. SIGMA 19 (2023), 010, 71 pages

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Digital Library of Periodicals of National Academy of Sciences of Ukraine
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author Costantino, Francesco
Gukov, Sergei
Putrov, Pavel
author_facet Costantino, Francesco
Gukov, Sergei
Putrov, Pavel
citation_txt Non-Semisimple TQFT's and BPS -Series. Francesco Costantino, Sergei Gukov and Pavel Putrov. SIGMA 19 (2023), 010, 71 pages
collection DSpace DC
container_title Symmetry, Integrability and Geometry: Methods and Applications
description We propose and, in some cases, prove a precise relation between 3-manifold invariants associated with quantum groups at roots of unity and at generic . Both types of invariants are labeled by extra data, which plays an important role in the proposed relation. Bridging the two sides - which until recently were developed independently, using very different methods - opens many new avenues. In one direction, it allows us to study (and perhaps even to formulate) -series invariants labeled by spinᶜ structures in terms of non-semisimple invariants. In the opposite direction, it offers new insights and perspectives on various elements of non-semisimple TQFT's, bringing the latter into one unifying framework with other invariants of knots and 3-manifolds that recently found realization in quantum field theory and in string theory.
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spelling Costantino, Francesco
Gukov, Sergei
Putrov, Pavel
2026-01-14T09:54:52Z
2023
Non-Semisimple TQFT's and BPS -Series. Francesco Costantino, Sergei Gukov and Pavel Putrov. SIGMA 19 (2023), 010, 71 pages
1815-0659
2020 Mathematics Subject Classification: TQFT
arXiv:2107.14238
https://nasplib.isofts.kiev.ua/handle/123456789/211874
https://doi.org/10.3842/SIGMA.2023.010
We propose and, in some cases, prove a precise relation between 3-manifold invariants associated with quantum groups at roots of unity and at generic . Both types of invariants are labeled by extra data, which plays an important role in the proposed relation. Bridging the two sides - which until recently were developed independently, using very different methods - opens many new avenues. In one direction, it allows us to study (and perhaps even to formulate) -series invariants labeled by spinᶜ structures in terms of non-semisimple invariants. In the opposite direction, it offers new insights and perspectives on various elements of non-semisimple TQFT's, bringing the latter into one unifying framework with other invariants of knots and 3-manifolds that recently found realization in quantum field theory and in string theory.
We would like to thank Francesco Benini, Christian Copetti, Boris Feigin, Azat Gainutdinov, Hiraku Nakajima, Sunghyuk Park, Du Pei, and Nicolai Reshetikhin for helpful discussions and the anonymous Referees for the valuable suggestions on the improvement of the paper. We also would like to thank the organizers of the 2019 conference “New Developments in Quantum Topology” at UC Berkeley, where the discussion on the relation between the two invariants was initiated. The work of S.G. is supported by the U.S. Department of Energy, Office of Science, Office of High Energy Physics, under Award No. DE-SC0011632, and by the National Science Foundation under Grant No. NSF DMS 1664227. The work of F.C. was supported by the French Agence Nationale de la Recherche via the ANR Project QUANTACT and by the Labex CIMI ANR-11-LABX-0040.
en
Інститут математики НАН України
Symmetry, Integrability and Geometry: Methods and Applications
Non-Semisimple TQFT's and BPS -Series
Article
published earlier
spellingShingle Non-Semisimple TQFT's and BPS -Series
Costantino, Francesco
Gukov, Sergei
Putrov, Pavel
title Non-Semisimple TQFT's and BPS -Series
title_full Non-Semisimple TQFT's and BPS -Series
title_fullStr Non-Semisimple TQFT's and BPS -Series
title_full_unstemmed Non-Semisimple TQFT's and BPS -Series
title_short Non-Semisimple TQFT's and BPS -Series
title_sort non-semisimple tqft's and bps -series
url https://nasplib.isofts.kiev.ua/handle/123456789/211874
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AT gukovsergei nonsemisimpletqftsandbpsseries
AT putrovpavel nonsemisimpletqftsandbpsseries