BPS spectra and 3-manifold invariants
Jan 23, 2017
85 pages
Published in:
- J.Knot Theor.Ramifications 29 (2020) 02, 2040003
- Published: Mar 17, 2020
e-Print:
- 1701.06567 [hep-th]
Report number:
- CALT-TH-2016-039
View in:
Citations per year
Abstract: (WSP)
We provide a physical definition of new homological invariants ℋa(M3) of 3-manifolds (possibly, with knots) labeled by abelian flat connections. The physical system in question involves a 6d fivebrane theory on M3 times a 2-disk, D2, whose Hilbert space of BPS states plays the role of a basic building block in categorification of various partition functions of 3d 𝒩 = 2 theory T[M3]: D2 × S1 half-index, S2 × S1 superconformal index, and S2 × S1 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 M3. 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.Note:
- v2: 80 pages, 7 figures, typos corrected, exposition improved with three newly added subsections (2.3, 2.4, 2.10)
- BPS spectrum
- 3-manifold
- invariant
- knot
- spectrum: BPS
- homology
- partition function
- topological
- factorization
- knot theory
References(98)
Figures(16)
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