A 3d-3d appetizer

Pei, Du; Ye, Ke

doi:10.1007/JHEP11(2016)008

Title: A 3d-3d appetizer

Abstract

Here, we test the 3d-3d correspondence for theories that are labeled by Lens spaces. We find a full agreement between the index of the 3d N=2 “Lens space theory” T [L(p, 1)] and the partition function of complex Chern-Simons theory on L(p, 1). In particular, for p = 1, we show how the familiar S³ partition function of Chern-Simons theory arises from the index of a free theory. For large p, we find that the index of T[L(p, 1)] becomes a constant independent of p. In addition, we study T[L(p, 1)] on the squashed three-sphere S_b³. This enables us to see clearly, at the level of partition function, to what extent G_C complex Chern-Simons theory can be thought of as two copies of Chern-Simons theory with compact gauge group G.

Authors:

Pei, Du ^[1]; Ye, Ke ^[1]

California Inst. of Technology (CalTech), Pasadena, CA (United States)

Publication Date:: Wed Nov 02 00:00:00 EDT 2016

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

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

OSTI Identifier:: 1360110

Grant/Contract Number:: SC0011632

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: 2016; Journal Issue: 11; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Chern-Simons theories; supersymmetric gauge theory; supersymmetry and duality; topological field theories

Citation Formats


                    Pei, Du, and Ye, Ke. A 3d-3d appetizer.  United States: N. p., 2016. 
Web.  doi:10.1007/JHEP11(2016)008.

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                    Pei, Du, & Ye, Ke. A 3d-3d appetizer.  United States.  https://doi.org/10.1007/JHEP11(2016)008

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                    Pei, Du, and Ye, Ke. Wed .  
"A 3d-3d appetizer".  United States.  https://doi.org/10.1007/JHEP11(2016)008.  https://www.osti.gov/servlets/purl/1360110.

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@article{osti_1360110,

  title        = {A 3d-3d appetizer},

  author       = {Pei, Du and Ye, Ke},

  abstractNote = {Here, we test the 3d-3d correspondence for theories that are labeled by Lens spaces. We find a full agreement between the index of the 3d N=2 “Lens space theory” T [L(p, 1)] and the partition function of complex Chern-Simons theory on L(p, 1). In particular, for p = 1, we show how the familiar S3 partition function of Chern-Simons theory arises from the index of a free theory. For large p, we find that the index of T[L(p, 1)] becomes a constant independent of p. In addition, we study T[L(p, 1)] on the squashed three-sphere Sb3. This enables us to see clearly, at the level of partition function, to what extent GC complex Chern-Simons theory can be thought of as two copies of Chern-Simons theory with compact gauge group G.},

  doi          = {10.1007/JHEP11(2016)008},

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

  number       = 11,

  volume       = 2016,

  place        = {United States},

  year         = {Wed Nov 02 00:00:00 EDT 2016},

  month        = {Wed Nov 02 00:00:00 EDT 2016}

}

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Works referenced in this record:

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Works referencing / citing this record:

Higher-form symmetries, Bethe vacua, and the 3d-3d correspondence
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Eckhard, Julius; Kim, Heeyeon; Schäfer-Nameki, Sakura
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Title: A 3d-3d appetizer

Abstract

Citation Formats

The gravity dual of supersymmetric gauge theories on a squashed three-sphere journal, November 2012

Vortices, instantons and branes journal, July 2003

Infinite-dimensional Lie algebras, theta functions and modular forms journal, August 1984

Dualities for 3d theories with tensor matter journal, December 2011

Complex Chern–Simons Theory at Level k via the 3d–3d Correspondence journal, June 2015

The geometry of supersymmetric partition functions journal, January 2014

Matrix models, topological strings, and supersymmetric gauge theories journal, November 2002

SUSY gauge theories on squashed three-spheres journal, May 2011

${\mathcal N} = 2$ SUPERSYMMETRIC THEORIES ON SQUASHED THREE-SPHERE journal, January 2013

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

Branes and quantization journal, January 2009

Indices for superconformal field theories in 3, 5 and 6 dimensions journal, February 2008

The gravity dual of supersymmetric gauge theories on a biaxially squashed three-sphere journal, January 2013

Vertices, vortices & interacting surface operators journal, June 2012

Non-Abelian localization for Chern-Simons theory journal, June 2005

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

Exact results for perturbative Chern–Simons theory with complex gauge group journal, January 2009

Localization on three-manifolds journal, October 2013

Chern-Simons Theory, Matrix Integrals, and Perturbative Three-Manifold Invariants journal, November 2004

Index for three dimensional superconformal field theories with general R-charge assignments journal, April 2011

3-Manifolds and 3d indices journal, January 2013

Gauge Theories Labelled by Three-Manifolds journal, December 2013

Generalized volume conjecture and the A -polynomials: The Neumann–Zagier potential function as a classical limit of the partition function journal, August 2007

Vortex Counting and Lagrangian 3-Manifolds journal, October 2011

Reshetikhin–Turaev Invariants of Seifert 3-Manifolds for Classical Simple lie Algebras journal, August 2004

2 + 1 dimensional gravity as an exactly soluble system journal, December 1988

Perturbative expansion of Chern-Simons theory with non-compact gauge group journal, October 1991

A TQFT from Quantum Teichmüller Theory journal, June 2014

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

Quantization of Chern-Simons gauge theory with complex gauge group journal, March 1991

Quantum field theory and the Jones polynomial journal, September 1989

Holomorphic blocks in three dimensions journal, December 2014

Branes and Quantization text, January 2008

Exact Results for Perturbative Chern-Simons Theory with Complex Gauge Group text, January 2009

Vortex Counting and Lagrangian 3-manifolds text, January 2010

Index for three dimensional superconformal field theories with general R-charge assignments text, January 2011

SUSY Gauge Theories on Squashed Three-Spheres text, January 2011

Dualities for 3d Theories with Tensor Matter text, January 2011

The gravity dual of supersymmetric gauge theories on a squashed three-sphere text, January 2011

3-Manifolds and 3d Indices preprint, January 2011

Holomorphic Blocks in Three Dimensions text, January 2012

3d-3d Correspondence Revisited text, January 2014

Complex Chern-Simons theory at level k via the 3d-3d correspondence preprint, January 2014

Vortices, Instantons and Branes text, January 2003

Non-Abelian Localization For Chern-Simons Theory text, January 2005

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

Equivariant Verlinde Algebra from Superconformal Index and Argyres–Seiberg Duality journal, January 2018

K-Decompositions and 3d Gauge Theories preprint, January 2013

Fivebranes and 3-manifold homology text, January 2016

Equivariant Verlinde algebra from superconformal index and Argyres-Seiberg duality text, January 2016

Symmetry enhancement and closing of knots in 3d/3d correspondence text, January 2018

Higher-Form Symmetries, Bethe Vacua, and the 3d-3d Correspondence text, January 2019

The gravity dual of supersymmetric gauge theories on a squashed three-sphere
journal, November 2012

Vortices, instantons and branes
journal, July 2003

Infinite-dimensional Lie algebras, theta functions and modular forms
journal, August 1984

Dualities for 3d theories with tensor matter
journal, December 2011

Complex Chern–Simons Theory at Level k via the 3d–3d Correspondence
journal, June 2015

The geometry of supersymmetric partition functions
journal, January 2014

Matrix models, topological strings, and supersymmetric gauge theories
journal, November 2002

SUSY gauge theories on squashed three-spheres
journal, May 2011

${\mathcal N} = 2$ SUPERSYMMETRIC THEORIES ON SQUASHED THREE-SPHERE
journal, January 2013

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

Branes and quantization
journal, January 2009

Indices for superconformal field theories in 3, 5 and 6 dimensions
journal, February 2008

The gravity dual of supersymmetric gauge theories on a biaxially squashed three-sphere
journal, January 2013

Vertices, vortices & interacting surface operators
journal, June 2012

Non-Abelian localization for Chern-Simons theory
journal, June 2005

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

Exact results for perturbative Chern–Simons theory with complex gauge group
journal, January 2009

Localization on three-manifolds
journal, October 2013

Chern-Simons Theory, Matrix Integrals, and Perturbative Three-Manifold Invariants
journal, November 2004

Index for three dimensional superconformal field theories with general R-charge assignments
journal, April 2011

3-Manifolds and 3d indices
journal, January 2013

Gauge Theories Labelled by Three-Manifolds
journal, December 2013

Generalized volume conjecture and the $A$ -polynomials: The Neumann–Zagier potential function as a classical limit of the partition function
journal, August 2007

Vortex Counting and Lagrangian 3-Manifolds
journal, October 2011

Reshetikhin–Turaev Invariants of Seifert 3-Manifolds for Classical Simple lie Algebras
journal, August 2004

2 + 1 dimensional gravity as an exactly soluble system
journal, December 1988

Perturbative expansion of Chern-Simons theory with non-compact gauge group
journal, October 1991

A TQFT from Quantum Teichmüller Theory
journal, June 2014

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

Quantization of Chern-Simons gauge theory with complex gauge group
journal, March 1991

Quantum field theory and the Jones polynomial
journal, September 1989

Holomorphic blocks in three dimensions
journal, December 2014

Branes and Quantization
text, January 2008

Exact Results for Perturbative Chern-Simons Theory with Complex Gauge Group
text, January 2009

Vortex Counting and Lagrangian 3-manifolds
text, January 2010

Index for three dimensional superconformal field theories with general R-charge assignments
text, January 2011

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text, January 2011

Dualities for 3d Theories with Tensor Matter
text, January 2011

The gravity dual of supersymmetric gauge theories on a squashed three-sphere
text, January 2011

3-Manifolds and 3d Indices
preprint, January 2011

Holomorphic Blocks in Three Dimensions
text, January 2012

3d-3d Correspondence Revisited
text, January 2014

Complex Chern-Simons theory at level k via the 3d-3d correspondence
preprint, January 2014

Vortices, Instantons and Branes
text, January 2003

Non-Abelian Localization For Chern-Simons Theory
text, January 2005

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

Equivariant Verlinde Algebra from Superconformal Index and Argyres–Seiberg Duality
journal, January 2018

K-Decompositions and 3d Gauge Theories
preprint, January 2013

Fivebranes and 3-manifold homology
text, January 2016

Equivariant Verlinde algebra from superconformal index and Argyres-Seiberg duality
text, January 2016

Symmetry enhancement and closing of knots in 3d/3d correspondence
text, January 2018

Higher-Form Symmetries, Bethe Vacua, and the 3d-3d Correspondence
text, January 2019