2017/01/23 by Gukov, Sergei, Pei, Du, Putrov, Pavel +1 · 15 citations
#FOS: Mathematics #FOS: Physical sciences #Geometric Topology (math.GT) #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph) #Quantum Algebra (math.QA)
paper · doi:10.48550/arxiv.1701.06567
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.