BPS spectra and 3-manifold invariants

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BPS spectra and 3-manifold invariants. / Gukov, Sergei; Pei, Du; Putrov, Pavel; Vafa, Cumrun.

In: Journal of Knot Theory and Its Ramifications, Vol. 29, No. 2, 2040003, 2020.

Research output: Contribution to journal/Conference contribution in journal/Contribution to newspaperJournal articleResearchpeer-review

Harvard

Gukov, S, Pei, D, Putrov, P & Vafa, C 2020, 'BPS spectra and 3-manifold invariants', Journal of Knot Theory and Its Ramifications, vol. 29, no. 2, 2040003. https://doi.org/10.1142/S0218216520400039

APA

Gukov, S., Pei, D., Putrov, P., & Vafa, C. (2020). BPS spectra and 3-manifold invariants. Journal of Knot Theory and Its Ramifications, 29(2), [2040003]. https://doi.org/10.1142/S0218216520400039

CBE

Gukov S, Pei D, Putrov P, Vafa C. 2020. BPS spectra and 3-manifold invariants. Journal of Knot Theory and Its Ramifications. 29(2):Article 2040003. https://doi.org/10.1142/S0218216520400039

MLA

Gukov, Sergei et al. "BPS spectra and 3-manifold invariants". Journal of Knot Theory and Its Ramifications. 2020. 29(2). https://doi.org/10.1142/S0218216520400039

Vancouver

Gukov S, Pei D, Putrov P, Vafa C. BPS spectra and 3-manifold invariants. Journal of Knot Theory and Its Ramifications. 2020;29(2). 2040003. https://doi.org/10.1142/S0218216520400039

Author

Gukov, Sergei ; Pei, Du ; Putrov, Pavel ; Vafa, Cumrun. / BPS spectra and 3-manifold invariants. In: Journal of Knot Theory and Its Ramifications. 2020 ; Vol. 29, No. 2.

Bibtex

@article{3e40dd9777e34a22b582f2166d8fca5e,
title = "BPS spectra and 3-manifold invariants",
abstract = "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.",
keywords = "3-manifold, BPS spectrum, invariant, knot",
author = "Sergei Gukov and Du Pei and Pavel Putrov and Cumrun Vafa",
year = "2020",
doi = "10.1142/S0218216520400039",
language = "English",
volume = "29",
journal = "Journal of Knot Theory and Its Ramifications",
issn = "0218-2165",
publisher = "World Scientific Publishing Co. Pte. Ltd.",
number = "2",

}

RIS

TY - JOUR

T1 - BPS spectra and 3-manifold invariants

AU - Gukov, Sergei

AU - Pei, Du

AU - Putrov, Pavel

AU - Vafa, Cumrun

PY - 2020

Y1 - 2020

N2 - 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.

AB - 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.

KW - 3-manifold

KW - BPS spectrum

KW - invariant

KW - knot

UR - http://www.scopus.com/inward/record.url?scp=85082075166&partnerID=8YFLogxK

U2 - 10.1142/S0218216520400039

DO - 10.1142/S0218216520400039

M3 - Journal article

AN - SCOPUS:85082075166

VL - 29

JO - Journal of Knot Theory and Its Ramifications

JF - Journal of Knot Theory and Its Ramifications

SN - 0218-2165

IS - 2

M1 - 2040003

ER -