Non-Semisimple TQFT's and BPS $q$-Series
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 . 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) -series invariants labeled by spin 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.
Keywords
Cite
@article{arxiv.2107.14238,
title = {Non-Semisimple TQFT's and BPS $q$-Series},
author = {Francesco Costantino and Sergei Gukov and Pavel Putrov},
journal= {arXiv preprint arXiv:2107.14238},
year = {2023}
}