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Non-Semisimple TQFT's and BPS $q$-Series

Authors :
Costantino, Francesco
Gukov, Sergei
Putrov, Pavel
Source :
SIGMA 19 (2023), 010, 71 pages
Publication Year :
2021

Abstract

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 $q$. 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 to study (and perhaps even to formulate) $q$-series invariants labeled by spin$^c$ 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.

Details

Database :
arXiv
Journal :
SIGMA 19 (2023), 010, 71 pages
Publication Type :
Report
Accession number :
edsarx.2107.14238
Document Type :
Working Paper
Full Text :
https://doi.org/10.3842/SIGMA.2023.010