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Supergroups, q-series and 3-manifolds
- Publication Year :
- 2020
-
Abstract
- We introduce supergroup analogues of 3-manifold invariants $\hat{Z}$, also known as homological blocks, which were previously considered for ordinary compact semisimple Lie groups. We focus on superunitary groups, and work out the case of SU(2|1) in details. Physically these invariants are realized as the index of BPS states of a system of intersecting fivebranes wrapping a 3-manifold in M-theory. As in the original case, the homological blocks are q-series with integer coefficients. We provide an explicit algorithm to calculate these q-series for a class of plumbed 3-manifolds and study quantum modularity and resurgence properties for some particular 3-manifolds. Finally, we conjecture a formula relating the $\hat{Z}$ invariants and the quantum invariants constructed from a non-semisimple category of representation of the unrolled version of a quantum supergroup.<br />Comment: 56 pages, 7 figures. v2: minor corrections in the text and formulas, references added
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.2009.14196
- Document Type :
- Working Paper