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