BPS spectra and 3-manifold invariants

Gukov, Sergei; Pei, Du; Putrov, Pavel; Vafa, Cumrun

doi:10.1142/s0218216520400039

BPS spectra and 3-manifold invariants

Journal Article · Tue Mar 17 00:00:00 EDT 2020 · Journal of Knot Theory and Its Ramifications

DOI:https://doi.org/10.1142/s0218216520400039· OSTI ID:1762744

Gukov, Sergei ^[1]; Pei, Du ^[2]; Putrov, Pavel ^[3]; Vafa, Cumrun ^[4]

California Institute of Technology (CalTech), Pasadena, CA (United States); Caltech
California Institute of Technology (CalTech), Pasadena, CA (United States); Univ. of Aarhus (Denmark)
Inst. for Advanced Study, Princeton, NJ (United States)
Harvard Univ., Cambridge, MA (United States)

We provide a physical definition of new homological invariants H_a(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. Here, we show how this works explicitly for many examples, including Lens spaces, circle fibrations over Riemann surfaces, and plumbed 3-manifolds.

View Accepted Manuscript (DOE)

Research Organization:: California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC0011632

OSTI ID:: 1762744

Journal Information:: Journal of Knot Theory and Its Ramifications, Journal Name: Journal of Knot Theory and Its Ramifications Journal Issue: 02 Vol. 29; ISSN 0218-2165

Publisher:: World ScientificCopyright Statement

Country of Publication:: United States

Language:: English

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