BPS spectra and 3-manifold invariants

DOI10.1142/S0218216520400039zbMATH Open1448.57020arXiv1701.06567OpenAlexW3004600674MaRDI QIDQ5111662

Author name not available (Why is that?)

Publication date: 27 May 2020

Published in: (Search for Journal in Brave)

Abstract: We provide a physical definition of new homological invariants $mathcal{H}_a(M_3)$ of 3-manifolds (possibly, with knots) labeled by abelian flat connections. The physical system in question involves a 6d fivebrane theory on $M_3$ times a 2-disk, $D^2$, whose Hilbert space of BPS states plays the role of a basic building block in categorification of various partition functions of 3d $mathcalN=2$ theory $T[M_3]$: $D^{2}imes{S}^1$ half-index, $S^{2}imes{S}^1$ superconformal index, and $S^{2}imes{S}^1$ topologically twisted index. The first partition function is labeled by a choice of boundary condition and provides a refinement of Chern-Simons (WRT) invariant. A linear combination of them in the unrefined limit gives the analytically continued WRT invariant of $M_3$. The last two can be factorized into the product of half-indices. We show how this works explicitly for many examples, including Lens spaces, circle fibrations over Riemann surfaces, and plumbed 3-manifolds.

Full work available at URL: https://arxiv.org/abs/1701.06567

zbMATH Keywords

No records found.

Mathematics Subject Classification ID

No records found.

This page was built for publication: BPS spectra and 3-manifold invariants

Report a bug (only for logged in users!)Click here to report a bug for this page (MaRDI item Q5111662)