3d-3d correspondence for mapping tori

Chun, Sungbong; Gukov, Sergei; Park, Sunghyuk; Sopenko, Nikita

doi:10.1007/jhep09(2020)152

Title: 3d-3d correspondence for mapping tori

Abstract

One of the main challenges in 3d-3d correspondence is that no existent approach offers a complete description of 3d N = 2 SCFT T [M3] — or, rather, a “collection of SCFTs” as we refer to it in the paper — for all types of 3-manifolds that include, for example, a 3-torus, Brieskorn spheres, and hyperbolic surgeries on knots. The goal of this paper is to overcome this challenge by a more systematic study of 3d-3d correspondence that, first of all, does not rely heavily on any geometric structure on M3 and, secondly, is not limited to a particular supersymmetric partition function of T [M3]. In particular, we propose to describe such “collection of SCFTs” in terms of 3d N = 2 gauge theories with “non-linear matter” fields valued in complex group manifolds. As a result, we are able to recover familiar 3-manifold invariants, such as Turaev torsion and WRT invariants, from twisted indices and half-indices of T [M3], and propose new tools to compute more recent q-series invariants Z * (M3) in the case of manifolds with b1> 0. Although we use genus-1 mappingmore »« less

Authors:

Chun, Sungbong ^[1]; Gukov, Sergei ^[2];

^[3]; Sopenko, Nikita ^[3]

Rutgers Univ., Piscataway, NJ (United States)
California Institute of Technology (CalTech), Pasadena, CA (United States); Max Planck Inst. for Mathematics, Bonn (Germany)
California Institute of Technology (CalTech), Pasadena, CA (United States)

Publication Date:: Wed Sep 23 00:00:00 EDT 2020

Research Org.:: Rutgers Univ., Piscataway, NJ (United States); California Institute of Technology (CalTech), Pasadena, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP); National Science Foundation (NSF)

OSTI Identifier:: 1706711

Grant/Contract Number:: SC0010008; SC0011632; DMS 1664240

Resource Type:: Accepted Manuscript

Journal Name:: Journal of High Energy Physics (Online)

Additional Journal Information:: Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2020; Journal Issue: 9; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Conformal Field Models in String Theory; Supersymmetric Effective Theories; Topological Field Theories

Citation Formats


                    Chun, Sungbong, Gukov, Sergei, Park, Sunghyuk, and Sopenko, Nikita. 3d-3d correspondence for mapping tori.  United States: N. p., 2020. 
Web.  doi:10.1007/jhep09(2020)152.

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                    Chun, Sungbong, Gukov, Sergei, Park, Sunghyuk, & Sopenko, Nikita. 3d-3d correspondence for mapping tori.  United States.  https://doi.org/10.1007/jhep09(2020)152

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                    Chun, Sungbong, Gukov, Sergei, Park, Sunghyuk, and Sopenko, Nikita. Wed .  
"3d-3d correspondence for mapping tori".  United States.  https://doi.org/10.1007/jhep09(2020)152.  https://www.osti.gov/servlets/purl/1706711.

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@article{osti_1706711,

  title        = {3d-3d correspondence for mapping tori},

  author       = {Chun, Sungbong and Gukov, Sergei and Park, Sunghyuk and Sopenko, Nikita},

  abstractNote = {One of the main challenges in 3d-3d correspondence is that no existent approach offers a complete description of 3d N = 2 SCFT T [M3] — or, rather, a “collection of SCFTs” as we refer to it in the paper — for all types of 3-manifolds that include, for example, a 3-torus, Brieskorn spheres, and hyperbolic surgeries on knots. The goal of this paper is to overcome this challenge by a more systematic study of 3d-3d correspondence that, first of all, does not rely heavily on any geometric structure on M3 and, secondly, is not limited to a particular supersymmetric partition function of T [M3]. In particular, we propose to describe such “collection of SCFTs” in terms of 3d N = 2 gauge theories with “non-linear matter” fields valued in complex group manifolds. As a result, we are able to recover familiar 3-manifold invariants, such as Turaev torsion and WRT invariants, from twisted indices and half-indices of T [M3], and propose new tools to compute more recent q-series invariants Z * (M3) in the case of manifolds with b1> 0. Although we use genus-1 mapping tori as our “case study,” many results and techniques readily apply to more general 3-manifolds, as we illustrate throughout the paper.},

  doi          = {10.1007/jhep09(2020)152},

  journal      = {Journal of High Energy Physics (Online)},

  number       = 9,

  volume       = 2020,

  place        = {United States},

  year         = {Wed Sep 23 00:00:00 EDT 2020},

  month        = {Wed Sep 23 00:00:00 EDT 2020}

}

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Title: 3d-3d correspondence for mapping tori

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Aspects of N = 2 supersymmetric gauge theories in three dimensions journal, August 1997

Walls, lines, and spectral dualities in 3d gauge theories journal, May 2014

Integration over the $u$-plane in Donaldson theory journal, January 1997

Topological quantum field theory journal, September 1988

A 3d gauge theory/quantum K-theory correspondence journal, January 2020

Four-Dimensional Wall-Crossing via Three-Dimensional Field Theory journal, July 2010

Supersymmetric partition functions and the three-dimensional A-twist journal, March 2017

The Elliptic Gamma Function and SL(3, Z)⋉Z3 journal, December 2000

Dual boundary conditions in 3d SCFT’s journal, May 2018

Chern-Simons-Witten invariants of lens spaces and torus bundles, and the semiclassical approximation journal, July 1992

Heegaard Floer homology and genus one, one-boundary component open books journal, October 2008

Gauge Theories and Macdonald Polynomials journal, November 2012

Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics journal, May 1997

Higher-form symmetries, Bethe vacua, and the 3d-3d correspondence journal, January 2020

A 3d-3d appetizer journal, November 2016

The Witten–Reshetikhin–Turaev invariant for links in finite order mapping tori I journal, January 2017

Bethe/gauge correspondence on curved spaces journal, January 2015

Gauge Theories Labelled by Three-Manifolds journal, December 2013

BPS invariants for Seifert manifolds journal, March 2020

Invariants of 3-manifolds via link polynomials and quantum groups journal, December 1991

Lectures on supersymmetric gauge theories and electric-magnetic duality journal, February 1996

Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial journal, March 2005

Complex Chern-Simons from M5-branes on the squashed three-sphere journal, November 2017

Superconformal index and 3d-3d correspondence for mapping cylinder/torus journal, January 2014

𝒩 = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals journal, October 2008

Ẑ invariants at rational τ journal, September 2019

3d modularity journal, October 2019

Remarks on the canonical quantization of the Chern-Simons-Witten theory journal, October 1989

Perturbative invariants of 3–manifolds with the first Betti number 1 journal, January 2010

Surgery in cusp neighborhoods and the geography of irreducible 4-manifolds journal, December 1994

Modifications and Cobounding Manifolds journal, January 1960

Limit values of the non-acyclic Reidemeister torsion for knots journal, January 2007

M5-branes on S 2 × M 4: Nahm’s equations and 4d topological sigma-models journal, September 2016

Mirror symmetry in three dimensional gauge theories journal, October 1996

Holomorphic disks and topological invariants for closed three-manifolds journal, January 2004

Trace as an Alternative Decategorification Functor journal, December 2014

A topologically twisted index for three-dimensional supersymmetric theories journal, July 2015

Issues in topological gauge theory journal, November 1998

Aspects of defects in 3d-3d correspondence journal, October 2016

A calculus for framed links inS 3 journal, February 1978

Special functions, conformal blocks, Bethe ansatz and SL(3, Z) journal, July 2001

3d-3d correspondence revisited journal, April 2016

$ {\text{SL}}\left( {2,\mathbb{R}} \right) $ Chern-Simons, Liouville, and gauge theory on duality walls journal, August 2011

Mirror symmetry and bosonization in 2d and 3d journal, July 2018

Examples of different 3-manifolds with the same invariants of Witten and Reshetikhin–Turaev journal, January 1993

Toroidal compactification without vector structure journal, February 1998

Vortex Counting and Lagrangian 3-Manifolds journal, October 2011

Asymptotic expansions of the Witten–Reshetikhin–Turaev invariants of mapping tori I journal, December 2018

Fivebranes and 4-Manifolds book, November 2016

N = 2 theories from cluster algebras journal, February 2014

BPS spectra and 3-manifold invariants journal, February 2020

A Representation of Orientable Combinatorial 3-Manifolds journal, November 1962

Notes on Certain (0,2) Correlation Functions journal, October 2005

Refined 3d-3d correspondence journal, April 2017

Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary journal, February 2003

Gauge theory and knot homologies journal, May 2007

Resurgence of the Kontsevich-Zagier series journal, January 2011

Holomorphic disks and three-manifolds invariants: Properties and applications journal, January 2004

Torus bundles not distinguished by TQFT invariants journal, January 2013

A Hyper-KÄHlerian Structure on Coadjoint Orbits of a Semisimple Complex Group journal, October 1990

Quantum field theory and the Jones polynomial journal, September 1989

Trisecting non-Lagrangian theories journal, November 2017

Equivariant Verlinde Formula from Fivebranes and Vortices journal, July 2017

The Skyrme model journal, September 1986

Triples, fluxes, and strings journal, January 2000

Gauge theory and knot homologies journal, May 2007

Chern-Simons invariants of 3-manifolds and representation spaces of knot groups journal, March 1990

A supersymmetric Skyrme model journal, February 2016

Gauge Theories Labelled by Three-Manifolds journal, December 2013

The Skyrme model journal, September 1986

D-branes, monopoles and Nahm equations journal, October 1997

A Hyper-KÄHlerian Structure on Coadjoint Orbits of a Semisimple Complex Group journal, October 1990

Special functions, conformal blocks, Bethe ansatz and SL(3, Z) text, January 2001

Vortex Counting and Lagrangian 3-manifolds text, January 2010

N = 2 dualities
journal, August 2012

On Heegaard Floer homology and Seifert fibered surgeries
conference, September 2004

HKT and OKT geometries on soliton black hole moduli spaces
journal, December 1997

Aspects of N = 2 supersymmetric gauge theories in three dimensions
journal, August 1997

Walls, lines, and spectral dualities in 3d gauge theories
journal, May 2014

Integration over the $u$-plane in Donaldson theory
journal, January 1997

Topological quantum field theory
journal, September 1988

A 3d gauge theory/quantum K-theory correspondence
journal, January 2020

Four-Dimensional Wall-Crossing via Three-Dimensional Field Theory
journal, July 2010

Supersymmetric partition functions and the three-dimensional A-twist
journal, March 2017

The Elliptic Gamma Function and SL(3, Z)⋉Z3
journal, December 2000

Dual boundary conditions in 3d SCFT’s
journal, May 2018

Chern-Simons-Witten invariants of lens spaces and torus bundles, and the semiclassical approximation
journal, July 1992

Heegaard Floer homology and genus one, one-boundary component open books
journal, October 2008

Gauge Theories and Macdonald Polynomials
journal, November 2012

Type IIB superstrings, BPS monopoles, and three-dimensional gauge dynamics
journal, May 1997

Higher-form symmetries, Bethe vacua, and the 3d-3d correspondence
journal, January 2020

A 3d-3d appetizer
journal, November 2016

The Witten–Reshetikhin–Turaev invariant for links in finite order mapping tori I
journal, January 2017

Bethe/gauge correspondence on curved spaces
journal, January 2015

Gauge Theories Labelled by Three-Manifolds
journal, December 2013

BPS invariants for Seifert manifolds
journal, March 2020

Invariants of 3-manifolds via link polynomials and quantum groups
journal, December 1991

Lectures on supersymmetric gauge theories and electric-magnetic duality
journal, February 1996

Three-Dimensional Quantum Gravity, Chern-Simons Theory, and the A-Polynomial
journal, March 2005

Complex Chern-Simons from M5-branes on the squashed three-sphere
journal, November 2017

Superconformal index and 3d-3d correspondence for mapping cylinder/torus
journal, January 2014

𝒩 = 6 superconformal Chern-Simons-matter theories, M2-branes and their gravity duals
journal, October 2008

Ẑ invariants at rational τ
journal, September 2019

3d modularity
journal, October 2019

Remarks on the canonical quantization of the Chern-Simons-Witten theory
journal, October 1989

Perturbative invariants of 3–manifolds with the first Betti number 1
journal, January 2010

Surgery in cusp neighborhoods and the geography of irreducible 4-manifolds
journal, December 1994

Modifications and Cobounding Manifolds
journal, January 1960

Limit values of the non-acyclic Reidemeister torsion for knots
journal, January 2007

M5-branes on S 2 × M 4: Nahm’s equations and 4d topological sigma-models
journal, September 2016

Mirror symmetry in three dimensional gauge theories
journal, October 1996

Holomorphic disks and topological invariants for closed three-manifolds
journal, January 2004

Trace as an Alternative Decategorification Functor
journal, December 2014

A topologically twisted index for three-dimensional supersymmetric theories
journal, July 2015

Issues in topological gauge theory
journal, November 1998

Aspects of defects in 3d-3d correspondence
journal, October 2016

A calculus for framed links inS 3
journal, February 1978

Special functions, conformal blocks, Bethe ansatz and SL(3, Z)
journal, July 2001

3d-3d correspondence revisited
journal, April 2016

$ {\text{SL}}\left( {2,\mathbb{R}} \right) $ Chern-Simons, Liouville, and gauge theory on duality walls
journal, August 2011

Mirror symmetry and bosonization in 2d and 3d
journal, July 2018

Examples of different 3-manifolds with the same invariants of Witten and Reshetikhin–Turaev
journal, January 1993

Toroidal compactification without vector structure
journal, February 1998

Vortex Counting and Lagrangian 3-Manifolds
journal, October 2011

Asymptotic expansions of the Witten–Reshetikhin–Turaev invariants of mapping tori I
journal, December 2018

Fivebranes and 4-Manifolds
book, November 2016

N = 2 theories from cluster algebras
journal, February 2014

BPS spectra and 3-manifold invariants
journal, February 2020

A Representation of Orientable Combinatorial 3-Manifolds
journal, November 1962

Notes on Certain (0,2) Correlation Functions
journal, October 2005

Refined 3d-3d correspondence
journal, April 2017

Absolutely graded Floer homologies and intersection forms for four-manifolds with boundary
journal, February 2003

Gauge theory and knot homologies
journal, May 2007

Resurgence of the Kontsevich-Zagier series
journal, January 2011

Holomorphic disks and three-manifolds invariants: Properties and applications
journal, January 2004

Torus bundles not distinguished by TQFT invariants
journal, January 2013

A Hyper-KÄHlerian Structure on Coadjoint Orbits of a Semisimple Complex Group
journal, October 1990

Quantum field theory and the Jones polynomial
journal, September 1989

Trisecting non-Lagrangian theories
journal, November 2017

Equivariant Verlinde Formula from Fivebranes and Vortices
journal, July 2017

The Skyrme model
journal, September 1986

Triples, fluxes, and strings
journal, January 2000

Gauge theory and knot homologies
journal, May 2007

Chern-Simons invariants of 3-manifolds and representation spaces of knot groups
journal, March 1990

A supersymmetric Skyrme model
journal, February 2016

Gauge Theories Labelled by Three-Manifolds
journal, December 2013

The Skyrme model
journal, September 1986

D-branes, monopoles and Nahm equations
journal, October 1997

A Hyper-KÄHlerian Structure on Coadjoint Orbits of a Semisimple Complex Group
journal, October 1990

Special functions, conformal blocks, Bethe ansatz and SL(3, Z)
text, January 2001

Vortex Counting and Lagrangian 3-manifolds
text, January 2010

Torus bundles not distinguished by TQFT invariants
text, January 2011

Fivebranes and 4-manifolds
preprint, January 2013

Trace as an alternative decategorification functor
text, January 2014