Supergroups, q-Series and 3-Manifolds - INSPIRE

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Supergroups, q-Series and 3-Manifolds

Francesca Ferrari
(
- SISSA, Trieste and
- INFN, Trieste and
- ICTP, Trieste
)
,
Pavel Putrov
(
- ICTP, Trieste
)

Sep 29, 2020

57 pages

Published in:

Annales Henri Poincare 25 (2024) 5, 2781-2837

Published: Feb 5, 2024

e-Print:

2009.14196 [hep-th]

DOI:

10.1007/s00023-023-01380-4

View in:

ADS Abstract Service

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Abstract: (Springer)

We introduce supergroup analogs of 3-manifold invariants

{\widehat{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

{\widehat{Z}}

invariants and the quantum invariants constructed from a non-semisimple category of representation of the unrolled version of a quantum supergroup.

Note:

56 pages, 7 figures. v2: minor corrections in the text and formulas, references added

M-theory
Chern-Simons theory
supergroup
3-manifolds
BPS states
category: representation
group: Lie
M-theory
SU(2|1)
BPS

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Figures(10)

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