High-temperature asymptotics of supersymmetric partition functions

Ardehali, Arash Arabi

doi:10.1007/JHEP07(2016)025

Title: High-temperature asymptotics of supersymmetric partition functions

Abstract

We study the supersymmetric partition function of 4d supersymmetric gauge theories with a U(1) R-symmetry on Euclidean S³ × S_β¹, with S³ the unit-radius squashed three-sphere, and β the circumference of the circle. For superconformal theories, this partition function coincides (up to a Casimir energy factor) with the 4d superconformal index. The partition function can be computed exactly using the supersymmetric localization of the gauge theory path-integral. It takes the form of an elliptic hypergeometric integral, which may be viewed as a matrix-integral over the moduli space of the holonomies of the gauge fields around S_β¹. At high temperatures (β → 0, corresponding to the hyperbolic limit of the elliptic hypergeometric integral) we obtain from the matrix-integral a quantum effective potential for the holonomies. The effective potential is proportional to the temperature. Therefore the high-temperature limit further localizes the matrix-integral to the locus of the minima of the potential. If the effective potential is positive semi-definite, the leading high-temperature asymptotics of the partition function is given by the formula of Di Pietro and Komargodski, and the subleading asymptotics is connected to the Coulomb branch dynamics on R³ × S¹. In theories where the effective potential is not positive semi-definite, themore »« less

Authors:

Ardehali, Arash Arabi ^[1]

Univ. of Michigan, Ann Arbor, MI (United States)

Publication Date:: Tue Jul 05 00:00:00 EDT 2016

Research Org.:: Univ. of Michigan, Ann Arbor, MI (United States)

Sponsoring Org.:: USDOE

OSTI Identifier:: 1326942

Grant/Contract Number:: SC0007859

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: 7; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Matrix Models; Supersymmetric gauge theory; Supersymmetry and Duality

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                    Ardehali, Arash Arabi. High-temperature asymptotics of supersymmetric partition functions.  United States: N. p., 2016. 
Web.  doi:10.1007/JHEP07(2016)025.

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                    Ardehali, Arash Arabi. High-temperature asymptotics of supersymmetric partition functions.  United States.  https://doi.org/10.1007/JHEP07(2016)025

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                    Ardehali, Arash Arabi. Tue .  
"High-temperature asymptotics of supersymmetric partition functions".  United States.  https://doi.org/10.1007/JHEP07(2016)025.  https://www.osti.gov/servlets/purl/1326942.

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@article{osti_1326942,

  title        = {High-temperature asymptotics of supersymmetric partition functions},

  author       = {Ardehali, Arash Arabi},

  abstractNote = {We study the supersymmetric partition function of 4d supersymmetric gauge theories with a U(1) R-symmetry on Euclidean S3 × Sβ1, with S3 the unit-radius squashed three-sphere, and β the circumference of the circle. For superconformal theories, this partition function coincides (up to a Casimir energy factor) with the 4d superconformal index. The partition function can be computed exactly using the supersymmetric localization of the gauge theory path-integral. It takes the form of an elliptic hypergeometric integral, which may be viewed as a matrix-integral over the moduli space of the holonomies of the gauge fields around Sβ1. At high temperatures (β → 0, corresponding to the hyperbolic limit of the elliptic hypergeometric integral) we obtain from the matrix-integral a quantum effective potential for the holonomies. The effective potential is proportional to the temperature. Therefore the high-temperature limit further localizes the matrix-integral to the locus of the minima of the potential. If the effective potential is positive semi-definite, the leading high-temperature asymptotics of the partition function is given by the formula of Di Pietro and Komargodski, and the subleading asymptotics is connected to the Coulomb branch dynamics on R3 × S1. In theories where the effective potential is not positive semi-definite, the Di Pietro-Komargodski formula needs to be modified. In particular, this modification occurs in the SU(2) theory of Intriligator-Seiberg-Shenker, and the SO(N) theory of Brodie-Cho-Intriligator, both believed to exhibit “misleading” anomaly matchings, and both believed to yield interacting superconformal field theories with c < a. Lastly, two new simple tests for dualities between 4d supersymmetric gauge theories emerge as byproducts of our analysis.},

  doi          = {10.1007/JHEP07(2016)025},

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

  number       = 7,

  volume       = 2016,

  place        = {United States},

  year         = {Tue Jul 05 00:00:00 EDT 2016},

  month        = {Tue Jul 05 00:00:00 EDT 2016}

}

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T$$ \overline{T} $$ deformation in SCFTs and integrable supersymmetric theories

Journal Article Ebert, Stephen ; Sun, Hao-Yu ; Sun, Zhengdi - Journal of High Energy Physics (Online)

We calculate the $ \mathcal{S} $-multiplets for two-dimensional Euclidean $ \mathcal{N} $ = (0, 2) and $ \mathcal{N} $ = (2, 2) superconformal field theories under the T$ \overline{T} $ deformation at leading order of perturbation theory in the deformation coupling. Then, from these $ \mathcal{N} $ = (0, 2) deformed multiplets, we calculate two- and three-point correlators. We show the $ \mathcal{N} $ = (0, 2) chiral ring’s elements do not flow under the T$ \overline{T} $ deformation. Specializing to integrable supersymmetric seed theories, such as $ \mathcal{N} $ = (2, 2) Landau-Ginzburg models, we use the thermodynamic Bethemore »« less
https://doi.org/10.1007/jhep09(2021)082

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Title: High-temperature asymptotics of supersymmetric partition functions

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Strongly Coupled Quantum Discrete Liouville Theory.¶I: Algebraic Approach and Duality journal, May 2001

(In)validity of large N orientifold equivalence journal, November 2006

Number of degrees of freedom, density of states and tachyons in string theory and CFT journal, July 1991

RG fixed points and flows in SQCD with adjoints journal, January 2004

An N = 2 superconformal fixed point with E6 global symmetry journal, December 1996

High-temperature expansion of supersymmetric partition functions journal, July 2015

Gauge Theories and Macdonald Polynomials journal, November 2012

Aspects of Supersymmetric Field Theories conference, January 2012

Superconformal Indices, Sasaki-Einstein Manifolds, and Cyclic Homologies preprint, January 2012

An Index for 4 dimensional Super Conformal Theories text, January 2005

Rigid Supersymmetric Theories in Curved Superspace text, January 2011

D--branes and Spinning Black Holes text, January 1996

An N=2 Superconformal Fixed Point with E_6 Global Symmetry text, January 1996

Relation between the 4d superconformal index and the S 3 partition function journal, September 2011

The N = 2 $$ \mathcal{N}=2 $$ Schur index from free fermions journal, January 2016

Aspects of Supersymmetric Field Theories journal, January 2010

The Superconformal Index of the E_6 SCFT text, January 2010

Relation between the 4d superconformal index and the S^3 partition function text, January 2011

Cardy formulae for SUSY theories in d = 4 and d = 6 journal, December 2014

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

Limits of elliptic hypergeometric integrals journal, October 2007

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

D-branes and spinning black holes journal, January 1997

Critical behavior at finite-temperature confinement transitions journal, December 1982

c − a from the N = 1 $$ \mathcal{N}=1 $$ superconformal index journal, December 2014

Misleading Anomaly Matchings? text, January 1998

Limits of elliptic hypergeometric integrals preprint, January 2006

IR free or interacting? A proposed diagnostic journal, December 2005

Microscopic origin of the Bekenstein-Hawking entropy journal, June 1996

Four Dimensional Superconformal Index from q -Deformed Two Dimensional Yang-Mills Theory journal, June 2011

The Casimir energy in curved space and its supersymmetric counterpart journal, July 2015

Chiral Duals of Non-Chiral SUSY Gauge Theories text, January 1995

The holographic Weyl anomaly journal, July 1998

Transformations of elliptic hypergeometric integrals journal, January 2010

3d dualities from 4d dualities for orthogonal groups journal, August 2013

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

Supersymmetric states of 𝒩 = 4 Yang-Mills from giant gravitons journal, December 2007

Cardy Formulae for SUSY Theories in d=4 and d=6 text, January 2014

Partition functions and elliptic genera from supergravity text, January 2006

Global Properties of Supersymmetric Theories and the Lens Space journal, July 2014

Reducing the 4d index to the S 3 partition function journal, December 2012

The superconformal index of the E 6 SCFT journal, August 2010

Localization on Hopf surfaces journal, August 2014

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

Constraints on the R-charges of free bound states from the Römelsberger index journal, July 2014

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

The modular properties and the integral representations of the multiple elliptic gamma functions text, January 2003

Strongly coupled quantum discrete Liouville theory. I: Algebraic approach and duality text, January 2000

RG Fixed Points and Flows in SQCD with Adjoints text, January 2003

Partition functions and elliptic genera from supergravity journal, January 2007

Superconformal indices, Sasaki-Einstein manifolds, and cyclic homologies journal, January 2014

Elliptic Hypergeometry of Supersymmetric Dualities II. Orthogonal Groups, Knots, and Vortices journal, December 2013

Elliptic Hypergeometry of Supersymmetric Dualities journal, March 2011

Rigid supersymmetric theories in curved superspace journal, June 2011

On the ISS model of dynamical SUSY breaking text, January 2010

3d dualities from 4d dualities text, January 2013

Seiberg dualities and the 3d/4d connection journal, July 2012

Chiral gauge dynamics and dynamical supersymmetry breaking text, January 2009

From 4d superconformal indices to 3d partition functions text, January 2011

Proposal for a simple model of dynamical SUSY breaking journal, January 1995

A crack in the conformal window journal, April 2013

Misleading anomaly matchings? journal, June 1998

Chiral gauge dynamics and dynamical supersymmetry breaking journal, July 2009

The modular properties and the integral representations of the multiple elliptic gamma functions journal, December 2004

An Index for 4 Dimensional Super Conformal Theories journal, June 2007

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

The $\mathcal{N}=1$ Chiral Multiplet on $T^2\times S^2$ and Supersymmetric Localization text, January 2013

Chiral duals of non-chiral SUSY gauge theories journal, October 1995

QCD and instantons at finite temperature journal, January 1981

Applications of the superconformal index for protected operators and q-hypergeometric identities to dual theories journal, September 2009

Elliptic hypergeometry of supersymmetric dualities text, January 2009

The exact Schur index of N = 4 $$ \mathcal{N}=4 $$ SYM journal, November 2015

Superconformal Indices of $${{\mathcal N}=4}$$ SYM Field Theories journal, November 2011

The Holographic Weyl anomaly text, January 1998

Counting chiral primaries in , superconformal field theories journal, July 2006

From 4d superconformal indices to 3d partition functions journal, October 2011

On the ISS model of dynamical SUSY breaking
journal, January 2011

Strongly Coupled Quantum Discrete Liouville Theory.¶I: Algebraic Approach and Duality
journal, May 2001

(In)validity of large $N$ orientifold equivalence
journal, November 2006

Number of degrees of freedom, density of states and tachyons in string theory and CFT
journal, July 1991

RG fixed points and flows in SQCD with adjoints
journal, January 2004

An N = 2 superconformal fixed point with E6 global symmetry
journal, December 1996

High-temperature expansion of supersymmetric partition functions
journal, July 2015

Gauge Theories and Macdonald Polynomials
journal, November 2012

Aspects of Supersymmetric Field Theories
conference, January 2012

Superconformal Indices, Sasaki-Einstein Manifolds, and Cyclic Homologies
preprint, January 2012

An Index for 4 dimensional Super Conformal Theories
text, January 2005

Rigid Supersymmetric Theories in Curved Superspace
text, January 2011

D--branes and Spinning Black Holes
text, January 1996

An N=2 Superconformal Fixed Point with E_6 Global Symmetry
text, January 1996

Relation between the 4d superconformal index and the S 3 partition function
journal, September 2011

The N = 2 $$ \mathcal{N}=2 $$ Schur index from free fermions
journal, January 2016

Aspects of Supersymmetric Field Theories
journal, January 2010

The Superconformal Index of the E_6 SCFT
text, January 2010

Relation between the 4d superconformal index and the S^3 partition function
text, January 2011

Cardy formulae for SUSY theories in d = 4 and d = 6
journal, December 2014

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

Limits of elliptic hypergeometric integrals
journal, October 2007

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

D-branes and spinning black holes
journal, January 1997

Critical behavior at finite-temperature confinement transitions
journal, December 1982

c − a from the N = 1 $$ \mathcal{N}=1 $$ superconformal index
journal, December 2014

Misleading Anomaly Matchings?
text, January 1998

Limits of elliptic hypergeometric integrals
preprint, January 2006

IR free or interacting? A proposed diagnostic
journal, December 2005

Microscopic origin of the Bekenstein-Hawking entropy
journal, June 1996

Four Dimensional Superconformal Index from $q$ -Deformed Two Dimensional Yang-Mills Theory
journal, June 2011

The Casimir energy in curved space and its supersymmetric counterpart
journal, July 2015

Chiral Duals of Non-Chiral SUSY Gauge Theories
text, January 1995

The holographic Weyl anomaly
journal, July 1998

Transformations of elliptic hypergeometric integrals
journal, January 2010

3d dualities from 4d dualities for orthogonal groups
journal, August 2013

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

Supersymmetric states of 𝒩 = 4 Yang-Mills from giant gravitons
journal, December 2007

Cardy Formulae for SUSY Theories in d=4 and d=6
text, January 2014

Partition functions and elliptic genera from supergravity
text, January 2006

Global Properties of Supersymmetric Theories and the Lens Space
journal, July 2014

Reducing the 4d index to the S 3 partition function
journal, December 2012

The superconformal index of the E 6 SCFT
journal, August 2010

Localization on Hopf surfaces
journal, August 2014

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

Constraints on the R-charges of free bound states from the Römelsberger index
journal, July 2014

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

The modular properties and the integral representations of the multiple elliptic gamma functions
text, January 2003

Strongly coupled quantum discrete Liouville theory. I: Algebraic approach and duality
text, January 2000

RG Fixed Points and Flows in SQCD with Adjoints
text, January 2003

Partition functions and elliptic genera from supergravity
journal, January 2007

Superconformal indices, Sasaki-Einstein manifolds, and cyclic homologies
journal, January 2014

Elliptic Hypergeometry of Supersymmetric Dualities II. Orthogonal Groups, Knots, and Vortices
journal, December 2013

Elliptic Hypergeometry of Supersymmetric Dualities
journal, March 2011

Rigid supersymmetric theories in curved superspace
journal, June 2011

On the ISS model of dynamical SUSY breaking
text, January 2010

3d dualities from 4d dualities
text, January 2013

Seiberg dualities and the 3d/4d connection
journal, July 2012

Chiral gauge dynamics and dynamical supersymmetry breaking
text, January 2009

From 4d superconformal indices to 3d partition functions
text, January 2011

Proposal for a simple model of dynamical SUSY breaking
journal, January 1995

A crack in the conformal window
journal, April 2013

Misleading anomaly matchings?
journal, June 1998

Chiral gauge dynamics and dynamical supersymmetry breaking
journal, July 2009

The modular properties and the integral representations of the multiple elliptic gamma functions
journal, December 2004

An Index for 4 Dimensional Super Conformal Theories
journal, June 2007

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

The $\mathcal{N}=1$ Chiral Multiplet on $T^2\times S^2$ and Supersymmetric Localization
text, January 2013

Chiral duals of non-chiral SUSY gauge theories
journal, October 1995

QCD and instantons at finite temperature
journal, January 1981

Applications of the superconformal index for protected operators and q-hypergeometric identities to dual theories
journal, September 2009

Elliptic hypergeometry of supersymmetric dualities
text, January 2009

The exact Schur index of N = 4 $$ \mathcal{N}=4 $$ SYM
journal, November 2015

Superconformal Indices of $${{\mathcal N}=4}$$ SYM Field Theories
journal, November 2011

The Holographic Weyl anomaly
text, January 1998

Counting chiral primaries in , superconformal field theories
journal, July 2006

From 4d superconformal indices to 3d partition functions
journal, October 2011

Supersymmetric states of N=4 Yang-Mills from giant gravitons
text, January 2006

Vertex operator algebras, Higgs branches, and modular differential equations
journal, August 2018

Flowing from 16 to 32 supercharges
journal, October 2018