BPS spectra and 3-manifold invariants

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  • Sergei Gukov, California Institute of Technology, Max-Planck-Institut für Mathematik
  • ,
  • Du Pei, California Institute of Technology
  • ,
  • Pavel Putrov, Abdus Salam International Centre for Theoretical Physics, Institute for Advanced Study
  • ,
  • Cumrun Vafa, Harvard University Jefferson Physical Laboratory

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 = 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.

Original languageEnglish
Article number2040003
JournalJournal of Knot Theory and Its Ramifications
Publication statusPublished - 2020

    Research areas

  • 3-manifold, BPS spectrum, invariant, knot

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