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 $q$. 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.

References in corpus (6)

• Generalized Global Symmetries
• Analytic Torsion, 3d Mirror Symmetry And Supergroup Chern-Simons Theories
• Cobordism invariants from BPS q-series
• The ADO Invariants are a q-Holonomic Family
• Non semi-simple sl(2) quantum invariants, spin case
• Rozansky-Witten theory, Localised then Tilted