Testing holography using lattice super-Yang-Mills theory on a 2-torus

Catterall, Simon; Jha, Raghav G.; Schaich, David; Wiseman, Toby

doi:10.1103/PhysRevD.97.086020

Title: Testing holography using lattice super-Yang-Mills theory on a 2-torus

Abstract

We consider maximally supersymmetric SU (N) Yang-Mills theory in Euclidean signature compactified on a flat two-dimensional torus with antiperiodic (“thermal”) fermion boundary conditions imposed on one cycle. At large N , holography predicts that this theory describes certain black hole solutions in type IIA and IIB supergravity, and we use lattice gauge theory to test this. Unlike the one-dimensional quantum mechanics case where there is only the dimensionless temperature to vary, here we emphasize there are two more parameters which determine the shape of the flat torus. While a rectangular Euclidean torus yields a thermal interpretation, allowing for skewed tori modifies the holographic dual black hole predictions and results in another direction to test holography. Our lattice calculations are based on a supersymmetric formulation naturally adapted to a particular skewing. Using this we perform simulations up to N = 16 with several lattice spacings for both skewed and rectangular tori. We observe the two expected black hole phases with their predicted behavior, with a transition between them that is consistent with the gravity prediction based on the Gregory-Laflamme transition.

Authors:: Catterall, Simon; Jha, Raghav G.; Schaich, David; Wiseman, Toby

Publication Date:: Mon Apr 30 00:00:00 EDT 2018

Research Org.:: Syracuse Univ., NY (United States)

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

OSTI Identifier:: 1435383

Alternate Identifier(s):: OSTI ID: 1501515

Grant/Contract Number:: SC0008669; SC0009998

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 97 Journal Issue: 8; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Catterall, Simon, Jha, Raghav G., Schaich, David, and Wiseman, Toby. Testing holography using lattice super-Yang-Mills theory on a 2-torus.  United States: N. p., 2018. 
Web.  doi:10.1103/PhysRevD.97.086020.

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                    Catterall, Simon, Jha, Raghav G., Schaich, David, & Wiseman, Toby. Testing holography using lattice super-Yang-Mills theory on a 2-torus.  United States.  https://doi.org/10.1103/PhysRevD.97.086020

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                    Catterall, Simon, Jha, Raghav G., Schaich, David, and Wiseman, Toby. Mon .  
"Testing holography using lattice super-Yang-Mills theory on a 2-torus".  United States.  https://doi.org/10.1103/PhysRevD.97.086020.

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@article{osti_1435383,

  title        = {Testing holography using lattice super-Yang-Mills theory on a 2-torus},

  author       = {Catterall, Simon and Jha, Raghav G. and Schaich, David and Wiseman, Toby},

  abstractNote = {We consider maximally supersymmetric SU (N) Yang-Mills theory in Euclidean signature compactified on a flat two-dimensional torus with antiperiodic (“thermal”) fermion boundary conditions imposed on one cycle. At large N , holography predicts that this theory describes certain black hole solutions in type IIA and IIB supergravity, and we use lattice gauge theory to test this. Unlike the one-dimensional quantum mechanics case where there is only the dimensionless temperature to vary, here we emphasize there are two more parameters which determine the shape of the flat torus. While a rectangular Euclidean torus yields a thermal interpretation, allowing for skewed tori modifies the holographic dual black hole predictions and results in another direction to test holography. Our lattice calculations are based on a supersymmetric formulation naturally adapted to a particular skewing. Using this we perform simulations up to N = 16 with several lattice spacings for both skewed and rectangular tori. We observe the two expected black hole phases with their predicted behavior, with a transition between them that is consistent with the gravity prediction based on the Gregory-Laflamme transition.},

  doi          = {10.1103/PhysRevD.97.086020},

  journal      = {Physical Review D},

  number       = 8,

  volume       = 97,

  place        = {United States},

  year         = {Mon Apr 30 00:00:00 EDT 2018},

  month        = {Mon Apr 30 00:00:00 EDT 2018}

}

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Title: Testing holography using lattice super-Yang-Mills theory on a 2-torus

Abstract

Citation Formats

A euclidean lattice construction of supersymmetric Yang-Mills theories with sixteen supercharges journal, September 2005

Anti-de Sitter space, thermal phase transition, and confinement in gauge theories journal, January 1998

On black hole thermodynamics from super Yang-Mills journal, July 2013

Lattice study of two-dimensional N = ( 2 , 2 ) super Yang-Mills theory at large N journal, September 2009

Nonperturbative study of dynamical SUSY breaking in N = ( 2 , 2 ) Yang-Mills theory journal, March 2018

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From twisted supersymmetry to orbifold lattices journal, January 2008

Topology change in general relativity, and the black-hole black-string transition journal, October 2005

Phases of one dimensional large N gauge theory in a 1/D expansion journal, February 2010

The flavoured BFSS model at high temperature journal, January 2017

Black hole thermodynamics from simulations of lattice Yang-Mills theory journal, August 2008

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Exact lattice supersymmetry journal, November 2009

Monte Carlo Studies of Supersymmetric Matrix Quantum Mechanics with Sixteen Supercharges at Finite Temperature journal, January 2008

Possible third-order phase transition in the large- N lattice gauge theory journal, January 1980

Precision lattice test of the gauge/gravity duality at large N journal, November 2016

Two-dimensional 𝒩 = (2, 2) super Yang-Mills theory on computer journal, September 2007

Large N field theories, string theory and gravity journal, January 2000

The BFSS model on the lattice journal, May 2016

A computer test of holographic flavour dynamics journal, May 2016

Toward holographic reconstruction of bulk geometry from lattice simulations journal, February 2018

N = ∞ phase transition in a class of exactly soluble model lattice gauge theories journal, June 1980

On the sign problem in 2D lattice super Yang-Mills journal, January 2012

Supersymmetry on a euclidean spacetime lattice 1. A target theory with four supercharges journal, August 2003

High temperature expansion in supersymmetric matrix quantum mechanics journal, December 2007

Towards lattice simulation of the gauge theory duals to black holes and hot strings journal, December 2007

Hagedorn Instability in Dimensionally Reduced Large- N Gauge Theories as Gregory-Laflamme and Rayleigh-Plateau Instabilities journal, August 2014

Schwarzschild Radius from Monte Carlo Calculation of the Wilson Loop in Supersymmetric Matrix Quantum Mechanics journal, May 2009

Black hole entropy from nonperturbative gauge theory journal, November 2001

Comments on thermodynamics of supersymmetric matrix models journal, September 2009

New Phases of Near-Extremal Branes on a Circle journal, September 2004

Parallel software for lattice N = 4 supersymmetric Yang–Mills theory journal, May 2015

Wilson Loops in Large N Field Theories journal, June 1998

Euclidean lattice simulation for dynamical supersymmetry breaking journal, May 2008

Extracting black hole physics from the lattice journal, April 2010

Black holes and the SYM phase diagram journal, January 1999

Nonlattice Simulation for Supersymmetric Gauge Theories in One Dimension journal, October 2007

The Large-N Limit of Superconformal Field Theories and Supergravity journal, January 1999

Simulations of Script N = 2 super Yang-Mills theory in two dimensions journal, March 2006

Supersymmetry on a euclidean spacetime lattice 2. Target theories with eight supercharges journal, December 2003

Phases of a two-dimensional large- N gauge theory on a torus journal, October 2011

The Hagedorn/Deconfinement Phase Transition in Weakly Coupled Large N Gauge Theories journal, January 2004

Black-hole–black-string phase transitions in thermal (1 + 1)-dimensional supersymmetric Yang–Mills theory on a circle journal, October 2004

Black Hole Thermodynamics from Calculations in Strongly Coupled Gauge Theory journal, February 2001

Thermal phases of D1-branes on a circle from lattice super Yang-Mills journal, December 2010

Black strings and p -branes are unstable journal, May 1993

A low temperature expansion for matrix quantum mechanics journal, May 2015

The phase structure of low dimensional large N gauge theories on tori journal, January 2006

First results from simulations of supersymmetric lattices journal, January 2009

Geometry of orbifolded supersymmetric lattice gauge theories journal, March 2008

Moduli dynamics as a predictive tool for thermal maximally supersymmetric Yang-Mills at large N journal, July 2015

Approximations for strongly-coupled supersymmetric quantum mechanics journal, April 2000

Critical point and scale setting in SU(3) plasma: An update journal, May 2015

Supergravity and the large N limit of theories with sixteen supercharges journal, July 1998

What lattice theorists can do for superstring/M-theory journal, August 2016

On stringy thresholds in SYM/AdS thermodynamics journal, April 1999

Higher Derivative Corrections to Black Hole Thermodynamics from Supersymmetric Matrix Quantum Mechanics journal, May 2009

Maximally supersymmetric Yang–Mills on the lattice journal, December 2017

Accelerating Dynamical-Fermion Computations Using the Rational Hybrid Monte Carlo Algorithm with Multiple Pseudofermion Fields journal, January 2007

Absence of sign problem in two-dimensional $ \mathcal{N} = \left( {2,2} \right) $ super Yang-Mills on lattice journal, January 2011

Phase structure of matrix quantum mechanics at finite temperature journal, October 2007

Lattice gauge theory for physics beyond the Standard Model journal, November 2019

A euclidean lattice construction of supersymmetric Yang-Mills theories with sixteen supercharges
journal, September 2005

Anti-de Sitter space, thermal phase transition, and confinement in gauge theories
journal, January 1998

On black hole thermodynamics from super Yang-Mills
journal, July 2013

Lattice study of two-dimensional $N = (2, 2)$ super Yang-Mills theory at large $N$
journal, September 2009

Nonperturbative study of dynamical SUSY breaking in $N = (2, 2)$ Yang-Mills theory
journal, March 2018

Dynamical aspects of large-N reduced models
journal, April 1999

Localised and nonuniform thermal states of super-Yang-Mills on a circle
journal, June 2017

Anomaly and sign problem in N=(2,2) SYM on polyhedra: Numerical analysis
journal, December 2016

From twisted supersymmetry to orbifold lattices
journal, January 2008

Topology change in general relativity, and the black-hole black-string transition
journal, October 2005

Phases of one dimensional large N gauge theory in a 1/D expansion
journal, February 2010

The flavoured BFSS model at high temperature
journal, January 2017

Black hole thermodynamics from simulations of lattice Yang-Mills theory
journal, August 2008

Vacuum energy of two-dimensional $N = (2, 2)$ super Yang-Mills theory
journal, June 2009

Exact lattice supersymmetry
journal, November 2009

Monte Carlo Studies of Supersymmetric Matrix Quantum Mechanics with Sixteen Supercharges at Finite Temperature
journal, January 2008

Possible third-order phase transition in the large- $N$ lattice gauge theory
journal, January 1980

Precision lattice test of the gauge/gravity duality at large $N$
journal, November 2016

Two-dimensional 𝒩 = (2, 2) super Yang-Mills theory on computer
journal, September 2007

Large N field theories, string theory and gravity
journal, January 2000

The BFSS model on the lattice
journal, May 2016

A computer test of holographic flavour dynamics
journal, May 2016

Toward holographic reconstruction of bulk geometry from lattice simulations
journal, February 2018

N = ∞ phase transition in a class of exactly soluble model lattice gauge theories
journal, June 1980

On the sign problem in 2D lattice super Yang-Mills
journal, January 2012

Supersymmetry on a euclidean spacetime lattice 1. A target theory with four supercharges
journal, August 2003

High temperature expansion in supersymmetric matrix quantum mechanics
journal, December 2007

Towards lattice simulation of the gauge theory duals to black holes and hot strings
journal, December 2007

Hagedorn Instability in Dimensionally Reduced Large- $N$ Gauge Theories as Gregory-Laflamme and Rayleigh-Plateau Instabilities
journal, August 2014

Schwarzschild Radius from Monte Carlo Calculation of the Wilson Loop in Supersymmetric Matrix Quantum Mechanics
journal, May 2009

Black hole entropy from nonperturbative gauge theory
journal, November 2001

Comments on thermodynamics of supersymmetric matrix models
journal, September 2009

New Phases of Near-Extremal Branes on a Circle
journal, September 2004

Parallel software for lattice $N = 4$ supersymmetric Yang–Mills theory
journal, May 2015

Wilson Loops in Large $N$ Field Theories
journal, June 1998

Euclidean lattice simulation for dynamical supersymmetry breaking
journal, May 2008

Extracting black hole physics from the lattice
journal, April 2010

Black holes and the SYM phase diagram
journal, January 1999

Nonlattice Simulation for Supersymmetric Gauge Theories in One Dimension
journal, October 2007

The Large-N Limit of Superconformal Field Theories and Supergravity
journal, January 1999

Simulations of Script N = 2 super Yang-Mills theory in two dimensions
journal, March 2006

Supersymmetry on a euclidean spacetime lattice 2. Target theories with eight supercharges
journal, December 2003

Phases of a two-dimensional large- $N$ gauge theory on a torus
journal, October 2011

The Hagedorn/Deconfinement Phase Transition in Weakly Coupled Large N Gauge Theories
journal, January 2004

Black-hole–black-string phase transitions in thermal (1 + 1)-dimensional supersymmetric Yang–Mills theory on a circle
journal, October 2004

Black Hole Thermodynamics from Calculations in Strongly Coupled Gauge Theory
journal, February 2001

Thermal phases of D1-branes on a circle from lattice super Yang-Mills
journal, December 2010

Black strings and p -branes are unstable
journal, May 1993

A low temperature expansion for matrix quantum mechanics
journal, May 2015

The phase structure of low dimensional large N gauge theories on tori
journal, January 2006

First results from simulations of supersymmetric lattices
journal, January 2009

Geometry of orbifolded supersymmetric lattice gauge theories
journal, March 2008

Moduli dynamics as a predictive tool for thermal maximally supersymmetric Yang-Mills at large N
journal, July 2015

Approximations for strongly-coupled supersymmetric quantum mechanics
journal, April 2000

Critical point and scale setting in SU(3) plasma: An update
journal, May 2015

Supergravity and the large $N$ limit of theories with sixteen supercharges
journal, July 1998

What lattice theorists can do for superstring/M-theory
journal, August 2016

On stringy thresholds in SYM/AdS thermodynamics
journal, April 1999

Higher Derivative Corrections to Black Hole Thermodynamics from Supersymmetric Matrix Quantum Mechanics
journal, May 2009

Maximally supersymmetric Yang–Mills on the lattice
journal, December 2017

Accelerating Dynamical-Fermion Computations Using the Rational Hybrid Monte Carlo Algorithm with Multiple Pseudofermion Fields
journal, January 2007

Absence of sign problem in two-dimensional $ \mathcal{N} = \left( {2,2} \right) $ super Yang-Mills on lattice
journal, January 2011

Phase structure of matrix quantum mechanics at finite temperature
journal, October 2007

Lattice gauge theory for physics beyond the Standard Model
journal, November 2019