A one-dimensional theory for Higgs branch operators

Dedushenko, Mykola; Pufu, Silviu S.; Yacoby, Ran

doi:10.1007/jhep03(2018)138

Title: A one-dimensional theory for Higgs branch operators

Abstract

We use supersymmetric localization to calculate correlation functions of half-BPS local operators in 3d N=4 superconformal field theories whose Lagrangian descriptions consist of vectormultiplets coupled to hypermultiplets. The operators we primarily study are certain twisted linear combinations of Higgs branch operators that can be inserted anywhere along a given line. These operators are constructed from the hypermultiplet scalars. They form a one-dimensional non-commutative operator algebra with topological correlation functions. The 2- and 3-point functions of Higgs branch operators in the full 3d N=4 theory can be simply inferred from the 1d topological algebra. After conformally mapping the 3d superconformal field theory from flat space to a round three-sphere, we preform supersymmetric localization using a supercharge that does not belong to any 3d N=2 subalgebra of the N=4 algebra. The result is a simple model that can be used to calculate correlation functions in the 1d topological algebra mentioned above. This model is a 1d Gaussian theory coupled to a matrix model, and it can be viewed as a gauge-fixed version of a topological gauged quantum mechanics. Our results generalize to non-conformal theories on S3 that contain real mass and Fayet-Iliopolous parameters. In conclusion, we also provide partial results in themore »« less

Authors:

Dedushenko, Mykola ^[1]; Pufu, Silviu S. ^[2]; Yacoby, Ran ^[3]

Princeton Univ., Princeton, NJ (United States). Joseph Henry Lab. of Physics; California Inst. of Technology (CalTech), Pasadena, CA (United States). Walter Burke Inst. for Theoretical Physics
Princeton Univ., Princeton, NJ (United States). Joseph Henry Lab. of Physics
Princeton Univ., Princeton, NJ (United States). Joseph Henry Lab. of Physics; Weizmann Inst. of Science, Rehovot (Israel). Dept. of Physics and Astrophysics

Publication Date:: Fri Mar 23 00:00:00 EDT 2018

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

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

OSTI Identifier:: 1499674

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: 2018; Journal Issue: 3; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Extended Supersymmetry; Supersymmetric Gauge Theory; Conformal Field Theory

Citation Formats


                    Dedushenko, Mykola, Pufu, Silviu S., and Yacoby, Ran. A one-dimensional theory for Higgs branch operators.  United States: N. p., 2018. 
Web.  doi:10.1007/jhep03(2018)138.

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                    Dedushenko, Mykola, Pufu, Silviu S., & Yacoby, Ran. A one-dimensional theory for Higgs branch operators.  United States.  https://doi.org/10.1007/jhep03(2018)138

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                    Dedushenko, Mykola, Pufu, Silviu S., and Yacoby, Ran. Fri .  
"A one-dimensional theory for Higgs branch operators".  United States.  https://doi.org/10.1007/jhep03(2018)138.  https://www.osti.gov/servlets/purl/1499674.

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@article{osti_1499674,

  title        = {A one-dimensional theory for Higgs branch operators},

  author       = {Dedushenko, Mykola and Pufu, Silviu S. and Yacoby, Ran},

  abstractNote = {We use supersymmetric localization to calculate correlation functions of half-BPS local operators in 3d N=4 superconformal field theories whose Lagrangian descriptions consist of vectormultiplets coupled to hypermultiplets. The operators we primarily study are certain twisted linear combinations of Higgs branch operators that can be inserted anywhere along a given line. These operators are constructed from the hypermultiplet scalars. They form a one-dimensional non-commutative operator algebra with topological correlation functions. The 2- and 3-point functions of Higgs branch operators in the full 3d N=4 theory can be simply inferred from the 1d topological algebra. After conformally mapping the 3d superconformal field theory from flat space to a round three-sphere, we preform supersymmetric localization using a supercharge that does not belong to any 3d N=2 subalgebra of the N=4 algebra. The result is a simple model that can be used to calculate correlation functions in the 1d topological algebra mentioned above. This model is a 1d Gaussian theory coupled to a matrix model, and it can be viewed as a gauge-fixed version of a topological gauged quantum mechanics. Our results generalize to non-conformal theories on S3 that contain real mass and Fayet-Iliopolous parameters. In conclusion, we also provide partial results in the 1d topological algebra associated with the Coulomb branch, where we calculate correlation functions of local operators built from the vectormultiplet scalars.},

  doi          = {10.1007/jhep03(2018)138},

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

  number       = 3,

  volume       = 2018,

  place        = {United States},

  year         = {Fri Mar 23 00:00:00 EDT 2018},

  month        = {Fri Mar 23 00:00:00 EDT 2018}

}

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Infinite Chiral Symmetry in Four Dimensions journal, January 2015

The Coulomb Branch of 3d $${\mathcal{N}= 4}$$ N = 4 Theories journal, June 2017

Supersymmetric field theories on three-manifolds journal, May 2013

tt * equations, localization and exact chiral rings in 4d N $$ \mathcal{N} $$ =2 SCFTs journal, February 2015

The exact superconformal R-symmetry extremizes Z journal, May 2012

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

A Path Integral Approach¶to the Kontsevich Quantization Formula journal, August 2000

Seiberg-Witten Prepotential from Instanton Counting journal, January 2003

Nonperturbative tests of three-dimensional dualities journal, October 2010

Deformation Quantization and Superconformal Symmetry in Three Dimensions journal, February 2017

Exact results for Wilson loops in superconformal Chern-Simons theories with matter journal, March 2010

Mirror symmetry in three dimensional gauge theories journal, October 1996

Exact Correlation Functions in S U ( 2 ) N = 2 Superconformal QCD journal, December 2014

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

Quantization of Integrable Systems and four Dimensional Gauge Theories conference, January 2012

Mirror symmetry in three-dimensional gauge theories, quivers and D-branes journal, May 1997

$S$-duality of boundary conditions in ${\mathcal N}=4$ super Yang-Mills theory journal, January 2009

Superprotected n -point correlation functions of local operators in 𝒩 = 4 super Yang-Mills journal, April 2009

The supersymmetric index in four dimensions journal, October 2017

Indices for 6 dimensional superconformal field theories journal, October 2017

Mirror symmetry and loop operators journal, November 2015

W $$ \mathcal{W} $$ symmetry in six dimensions journal, May 2015

Analytic continuation of Chern-Simons theory book, January 2010

Three-point functions of chiral operators in $D = 4 , \mathcal{N} = 4$ SYM at large $N$ journal, January 1998

Introduction to localization in quantum field theory journal, October 2017

Exact correlators of BPS Operators from the 3d superconformal bootstrap journal, March 2015

Supersymmetric localization in two dimensions journal, October 2017

Contact terms, unitarity, and F -maximization in three-dimensional superconformal theories journal, October 2012

A non-renormalization theorem for chiral primary 3-point functions journal, July 2012

Mirror symmetry in three-dimensional gauge theories, and D-brane moduli spaces journal, May 1997

Notes on SUSY gauge theories on three-sphere journal, March 2011

Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops journal, May 2012

Chiral algebras of class S $$ \mathcal{S} $$ journal, May 2015

Correlation functions of Coulomb branch operators journal, January 2017

Localization of the four-dimensional $ \mathcal{N}=4 $ SYM to a two-sphere and 1/8 BPS Wilson loops journal, December 2012

On mirror symmetry in three dimensional Abelian gauge theories journal, April 1999

Localization of gauge theory on a four-sphere and supersymmetric Wilson loops text, January 2007

Superprotected n-point correlation functions of local operators in N=4 super Yang-Mills text, January 2009

Localization of the four-dimensional N=4 SYM to a two-sphere and 1/8 BPS Wilson loops text, January 2009

Quantization of Integrable Systems and Four Dimensional Gauge Theories text, January 2009

Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter text, January 2009

Notes on SUSY Gauge Theories on Three-Sphere text, January 2010

From Necklace Quivers to the F-theorem, Operator Counting, and T(U(N)) text, January 2011

A non-renormalization theorem for chiral primary 3-point functions text, January 2012

Contact Terms, Unitarity, and F-Maximization in Three-Dimensional Superconformal Theories text, January 2012

Supersymmetric Field Theories on Three-Manifolds text, January 2012

Infinite Chiral Symmetry in Four Dimensions text, January 2013

Deformation quantization and superconformal symmetry in three dimensions text, January 2016

A Ten-Dimensional Super-Yang-Mills Action with Off-Shell Supersymmetry text, January 1993

Mirror Symmetry in Three Dimensional Gauge Theories text, January 1996

Mirror Symmetry in Three-Dimensional Gauge Theories, Quivers and D-branes text, January 1996

Aspects of N=2 Supersymmetric Gauge Theories in Three Dimensions text, January 1997

On exact correlation functions in SU(N) N=2 superconformal QCD text, January 2015

Superprotected n-point correlation functions of local operators in N=4 super Yang-Mills text, January 2009

Matrix models for 5d super Yang-Mills text, January 2016

AdS4/CFT3 for unprotected operators journal, July 2018

On Mellin amplitudes in SCFTs with eight supercharges journal, July 2018

Schur correlation functions on S3 × S1 journal, July 2019

M-theory reconstruction from (2,0) CFT and the chiral algebra conjecture journal, August 2018

Chern-Simons theory from M5-branes and calibrated M2-branes journal, August 2019

Coulomb branch quantization and abelianized monopole bubbling journal, October 2019

SQED 3 and SQCD 3 : Phase transitions and integrability journal, September 2019

Solving M-theory with the Conformal Bootstrap text, January 2017

The Infrared Fixed Points of 3d $\mathcal{N}=4$ $USp(2N)$ SQCD Theories text, January 2018

On Mellin Amplitudes in SCFTs with Eight Supercharges text, January 2018

M-Theory Reconstruction from (2,0) CFT and the Chiral Algebra Conjecture text, January 2018

The Conformal Bootstrap: Theory, Numerical Techniques, and Applications text, January 2018

Chern-Simons theory from M5-branes and calibrated M2-branes text, January 2018

Sphere correlation functions and Verma modules journal, February 2020

Line defects in three dimensional mirror symmetry beyond linear quivers journal, July 2022

Non-unitary TQFTs from 3D $$ \mathcal{N} $$ = 4 rank 0 SCFTs journal, August 2021

Topological correlators and surface defects from equivariant cohomology journal, September 2020

Algebras, traces, and boundary correlators in $$ \mathcal{N} $$ = 4 SYM journal, December 2021

SUSY Localization for Coulomb Branch Operators in Omega-Deformed 3d $$\mathcal {N}$$ = 4 Gauge Theories journal, December 2022

Non-Abelian mirror symmetry beyond the chiral ring journal, April 2020

On Lagrangian description of Borel resummation preprint, January 2017

Chern-Simons theory from M5-branes and calibrated M2-branes text, January 2018

Infinite Chiral Symmetry in Four Dimensions
journal, January 2015

The Coulomb Branch of 3d $${\mathcal{N}= 4}$$ N = 4 Theories
journal, June 2017

Supersymmetric field theories on three-manifolds
journal, May 2013

tt * equations, localization and exact chiral rings in 4d N $$ \mathcal{N} $$ =2 SCFTs
journal, February 2015

The exact superconformal R-symmetry extremizes Z
journal, May 2012

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

A Path Integral Approach¶to the Kontsevich Quantization Formula
journal, August 2000

Seiberg-Witten Prepotential from Instanton Counting
journal, January 2003

Nonperturbative tests of three-dimensional dualities
journal, October 2010

Deformation Quantization and Superconformal Symmetry in Three Dimensions
journal, February 2017

Exact results for Wilson loops in superconformal Chern-Simons theories with matter
journal, March 2010

Mirror symmetry in three dimensional gauge theories
journal, October 1996

Exact Correlation Functions in $S U (2)$ $N = 2$ Superconformal QCD
journal, December 2014

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

Quantization of Integrable Systems and four Dimensional Gauge Theories
conference, January 2012

Mirror symmetry in three-dimensional gauge theories, quivers and D-branes
journal, May 1997

$S$-duality of boundary conditions in ${\mathcal N}=4$ super Yang-Mills theory
journal, January 2009

Superprotected n -point correlation functions of local operators in 𝒩 = 4 super Yang-Mills
journal, April 2009

The supersymmetric index in four dimensions
journal, October 2017

Indices for 6 dimensional superconformal field theories
journal, October 2017

Mirror symmetry and loop operators
journal, November 2015

W $$ \mathcal{W} $$ symmetry in six dimensions
journal, May 2015

Analytic continuation of Chern-Simons theory
book, January 2010

Three-point functions of chiral operators in $D = 4 , \mathcal{N} = 4$ SYM at large $N$
journal, January 1998

Introduction to localization in quantum field theory
journal, October 2017

Exact correlators of BPS Operators from the 3d superconformal bootstrap
journal, March 2015

Supersymmetric localization in two dimensions
journal, October 2017

Contact terms, unitarity, and F -maximization in three-dimensional superconformal theories
journal, October 2012

A non-renormalization theorem for chiral primary 3-point functions
journal, July 2012

Mirror symmetry in three-dimensional gauge theories, and D-brane moduli spaces
journal, May 1997

Notes on SUSY gauge theories on three-sphere
journal, March 2011

Localization of Gauge Theory on a Four-Sphere and Supersymmetric Wilson Loops
journal, May 2012

Chiral algebras of class S $$ \mathcal{S} $$
journal, May 2015

Correlation functions of Coulomb branch operators
journal, January 2017

Localization of the four-dimensional $ \mathcal{N}=4 $ SYM to a two-sphere and 1/8 BPS Wilson loops
journal, December 2012

On mirror symmetry in three dimensional Abelian gauge theories
journal, April 1999

Localization of gauge theory on a four-sphere and supersymmetric Wilson loops
text, January 2007

Superprotected n-point correlation functions of local operators in N=4 super Yang-Mills
text, January 2009

Localization of the four-dimensional N=4 SYM to a two-sphere and 1/8 BPS Wilson loops
text, January 2009

Quantization of Integrable Systems and Four Dimensional Gauge Theories
text, January 2009

Exact Results for Wilson Loops in Superconformal Chern-Simons Theories with Matter
text, January 2009

Notes on SUSY Gauge Theories on Three-Sphere
text, January 2010

From Necklace Quivers to the F-theorem, Operator Counting, and T(U(N))
text, January 2011

A non-renormalization theorem for chiral primary 3-point functions
text, January 2012

Contact Terms, Unitarity, and F-Maximization in Three-Dimensional Superconformal Theories
text, January 2012

Supersymmetric Field Theories on Three-Manifolds
text, January 2012

Infinite Chiral Symmetry in Four Dimensions
text, January 2013

Deformation quantization and superconformal symmetry in three dimensions
text, January 2016

A Ten-Dimensional Super-Yang-Mills Action with Off-Shell Supersymmetry
text, January 1993

Mirror Symmetry in Three Dimensional Gauge Theories
text, January 1996

Mirror Symmetry in Three-Dimensional Gauge Theories, Quivers and D-branes
text, January 1996

Aspects of N=2 Supersymmetric Gauge Theories in Three Dimensions
text, January 1997

On exact correlation functions in SU(N) N=2 superconformal QCD
text, January 2015

Superprotected n-point correlation functions of local operators in N=4 super Yang-Mills
text, January 2009

Matrix models for 5d super Yang-Mills
text, January 2016

AdS4/CFT3 for unprotected operators
journal, July 2018

On Mellin amplitudes in SCFTs with eight supercharges
journal, July 2018

Schur correlation functions on S3 × S1
journal, July 2019

M-theory reconstruction from (2,0) CFT and the chiral algebra conjecture
journal, August 2018

Chern-Simons theory from M5-branes and calibrated M2-branes
journal, August 2019

Coulomb branch quantization and abelianized monopole bubbling
journal, October 2019

${SQED}_{3}$ and ${SQCD}_{3}$ : Phase transitions and integrability
journal, September 2019

Solving M-theory with the Conformal Bootstrap
text, January 2017

The Infrared Fixed Points of 3d $\mathcal{N}=4$ $USp(2N)$ SQCD Theories
text, January 2018

On Mellin Amplitudes in SCFTs with Eight Supercharges
text, January 2018

M-Theory Reconstruction from (2,0) CFT and the Chiral Algebra Conjecture
text, January 2018

The Conformal Bootstrap: Theory, Numerical Techniques, and Applications
text, January 2018

Chern-Simons theory from M5-branes and calibrated M2-branes
text, January 2018

Sphere correlation functions and Verma modules
journal, February 2020

Line defects in three dimensional mirror symmetry beyond linear quivers
journal, July 2022

Non-unitary TQFTs from 3D $$ \mathcal{N} $$ = 4 rank 0 SCFTs
journal, August 2021

Topological correlators and surface defects from equivariant cohomology
journal, September 2020

Algebras, traces, and boundary correlators in $$ \mathcal{N} $$ = 4 SYM
journal, December 2021

SUSY Localization for Coulomb Branch Operators in Omega-Deformed 3d $$\mathcal {N}$$ = 4 Gauge Theories
journal, December 2022

Non-Abelian mirror symmetry beyond the chiral ring
journal, April 2020

On Lagrangian description of Borel resummation
preprint, January 2017

Chern-Simons theory from M5-branes and calibrated M2-branes
text, January 2018

From VOAs to short star products in SCFT
preprint, January 2019

4d/2d $\rightarrow $ 3d/1d: A song of protected operator algebras
preprint, January 2019

Taming Defects in $\mathcal{N}=4$ Super-Yang-Mills
text, January 2020