The classical double copy in three spacetime dimensions

González, Mariana Carrillo; Melcher, Brandon; Ratliff, Kenneth; Watson, Scott; White, Chris D.

doi:10.1007/jhep07(2019)167

Title: The classical double copy in three spacetime dimensions

Abstract

Abstract The double copy relates scattering amplitudes in gauge and gravity theories, and has also been extended to classical solutions. In this paper, we study solutions in three spacetime dimensions, where the double copy may be expected to be problematic due to the absence of propagating degrees of freedom for the graviton, and the lack of a Newtonian limit. In particular, we examine the double copy of a gauge theory point charge. This is a vacuum solution in gauge theory, but leads to a non-vacuum solution in gravity, which we show is consistent with previously derived constraints. Furthermore, we successfully interpret the non-trivial stress-energy tensor on the gravity side as arising from a dilaton profile, and the Newtonian description of a point charge emerges as expected in the appropriate limit. Thus, our results provide a non-trivial cross-check of the classical Kerr-Schild double copy.

Authors:

^[1]; Melcher, Brandon ^[2]; Ratliff, Kenneth ^[2]; Watson, Scott ^[2]; White, Chris D. ^[3]

Univ. of Pennsylvania, Philadelphia, PA (United States)
Syracuse Univ., NY (United States)
Queen Mary Univ. of London (United Kingdom)

Publication Date:: Mon Jul 29 00:00:00 EDT 2019

Research Org.:: Univ. of California, Oakland, CA (United States); Univ. of Pennsylvania, Philadelphia, PA (United States)

Sponsoring Org.:: USDOE Office of Science (SC); Science and Technology Facilities Council (STFC); Marie Sklodowska-Curie Grant

OSTI Identifier:: 1612916

Alternate Identifier(s):: OSTI ID: 1905120

Grant/Contract Number:: SC0018298; SC0013528; ST/P00754/1; 764850; FG02-85ER40237

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: 2019; Journal Issue: 7; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; physics; black holes; gauge-gravity correspondence; scattering amplitudes

Citation Formats


                    González, Mariana Carrillo, Melcher, Brandon, Ratliff, Kenneth, Watson, Scott, and White, Chris D. The classical double copy in three spacetime dimensions.  United States: N. p., 2019. 
Web.  doi:10.1007/jhep07(2019)167.

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                    González, Mariana Carrillo, Melcher, Brandon, Ratliff, Kenneth, Watson, Scott, & White, Chris D. The classical double copy in three spacetime dimensions.  United States.  https://doi.org/10.1007/jhep07(2019)167

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                    González, Mariana Carrillo, Melcher, Brandon, Ratliff, Kenneth, Watson, Scott, and White, Chris D. Mon .  
"The classical double copy in three spacetime dimensions".  United States.  https://doi.org/10.1007/jhep07(2019)167.  https://www.osti.gov/servlets/purl/1612916.

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@article{osti_1612916,

  title        = {The classical double copy in three spacetime dimensions},

  author       = {González, Mariana Carrillo and Melcher, Brandon and Ratliff, Kenneth and Watson, Scott and White, Chris D.},

  abstractNote = {Abstract The double copy relates scattering amplitudes in gauge and gravity theories, and has also been extended to classical solutions. In this paper, we study solutions in three spacetime dimensions, where the double copy may be expected to be problematic due to the absence of propagating degrees of freedom for the graviton, and the lack of a Newtonian limit. In particular, we examine the double copy of a gauge theory point charge. This is a vacuum solution in gauge theory, but leads to a non-vacuum solution in gravity, which we show is consistent with previously derived constraints. Furthermore, we successfully interpret the non-trivial stress-energy tensor on the gravity side as arising from a dilaton profile, and the Newtonian description of a point charge emerges as expected in the appropriate limit. Thus, our results provide a non-trivial cross-check of the classical Kerr-Schild double copy.},

  doi          = {10.1007/jhep07(2019)167},

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

  number       = 7,

  volume       = 2019,

  place        = {United States},

  year         = {Mon Jul 29 00:00:00 EDT 2019},

  month        = {Mon Jul 29 00:00:00 EDT 2019}

}

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Chacón, Erick; Nagy, Silvia; White, Chris D.
arXiv
DOI: 10.48550/arxiv.2103.16441

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Title: The classical double copy in three spacetime dimensions

Abstract

Citation Formats

Gravity as Gauge Theory Squared: A Ghost Story journal, November 2018

Black hole in three-dimensional spacetime journal, September 1992

Einstein's theory in a three-dimensional space-time journal, August 1984

Geometry of the 2+1 black hole journal, August 1993

Classical space–times from the S-matrix journal, December 2013

The double copy: Bremsstrahlung and accelerating black holes journal, June 2016

New formulas for amplitudes from higher-dimensional operators journal, February 2017

The classical double copy for Taub–NUT spacetime journal, November 2015

Transcendence of the Law of Baryon-Number Conservation in Black-Hole Physics journal, February 1972

One-loop four-point amplitudes in pure and matter-coupled $ \mathcal{N}\leq 4 $ supergravity journal, March 2013

Black holes in the Brans-Dicke: Theory of gravitation journal, June 1972

Explicit BCJ numerators from pure spinors journal, July 2011

Extended solutions for the biadjoint scalar field journal, December 2017

Two-loop four-gluon amplitudes in N = 4 super-Yang-Mills journal, May 1997

Perturbative gravity from QCD amplitudes journal, June 1999

Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order text, January 2019

Color-kinematics duality in multi-Regge kinematics and dimensional reduction journal, October 2013

Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order journal, May 2019

Monodromy and Jacobi-like relations for color-ordered amplitudes journal, June 2010

The kinematic algebra from the self-dual sector journal, July 2011

Gravity as the square of Yang–Mills? journal, September 2015

Next-to-soft corrections to high energy scattering in QCD and gravity journal, January 2017

Dyson pairs and zero mass black holes journal, September 1996

Unifying relations for scattering amplitudes journal, February 2018

Color-kinematics duality for QCD amplitudes journal, January 2016

Gravity Amplitudes as Generalized Double Copies of Gauge-Theory Amplitudes journal, May 2017

Algebras for amplitudes journal, June 2012

Perturbative Quantum Gravity as a Double Copy of Gauge Theory journal, August 2010

Exact Solutions of Einstein's Field Equations book, January 2009

Dual identities inside the gluon and the graviton scattering amplitudes journal, June 2010

On the relationship between Yang-Mills theory and gravity and its implication for ultraviolet divergences journal, October 1998

String-inspired BCJ numerators for one-loop MHV amplitudes journal, January 2016

Perturbative spacetimes from Yang-Mills theory journal, April 2017

Ultraviolet Properties of N = 4 Supergravity at Four Loops journal, December 2013

Factorization properties of soft graviton amplitudes journal, May 2011

Three-dimensional classical spacetimes journal, July 1986

Color-kinematics duality and double-copy construction for amplitudes from higher-dimension operators journal, October 2012

Type D spacetimes and the Weyl double copy journal, February 2019

Black holes and the double copy journal, December 2014

Relationship between gravity and gauge scattering in the high energy limit journal, January 2013

The Kerr-Schild double copy in curved spacetime journal, December 2017

A relation between tree amplitudes of closed and open strings journal, May 1986

Dual-color decompositions at one-loop level in Yang-Mills theory journal, June 2014

Color-kinematics duality and the Regge limit of inelastic amplitudes journal, April 2013

The classical double copy in maximally symmetric spacetimes journal, April 2018

Biadjoint wires journal, January 2019

Spinning BTZ black hole versus Kerr black hole: A closer look journal, February 1999

Gauge amplitude identities by on-shell recursion relation in S-matrix program journal, January 2011

N = 4 Yang-Mills and N = 8 supergravity as limits of string theories journal, May 1982

Exact solutions for the biadjoint scalar field journal, December 2016

Are all supergravity theories Yang–Mills squared? journal, September 2018

Minimal Basis for Gauge Theory Amplitudes journal, October 2009

The self-dual classical double copy, and the Eguchi-Hanson instanton journal, January 2019

Inelastic black hole scattering from charged scalar amplitudes journal, March 2018

Two-loop five-point amplitudes of super Yang-Mills and supergravity in pure spinor superspace journal, October 2015

Chiral squaring journal, July 2016

All-loop infrared-divergent behavior of most-subleading-color gauge-theory amplitudes journal, April 2013

Towards one-loop SYM amplitudes from the pure spinor BRST cohomology: Towards one-loop SYM amplitudes from the pure spinor BRST cohomology journal, January 2015

Integrand oxidation and one-loop colour-dual numerators in $ \mathcal{N}=4 $ gauge theory journal, July 2013

The structure of n-point one-loop open superstring amplitudes journal, August 2014

BCJ duality and the double copy in the soft limit journal, February 2013

Yang-Mills Origin of Gravitational Symmetries journal, December 2014

Gravitational radiation from color-kinematics duality journal, November 2018

A double copy for N = 2 $$ \mathcal{N}=2 $$ supergravity: a linearised tale told on-shell journal, October 2016

Spontaneously broken Yang-Mills-Einstein supergravities as double copies journal, June 2017

Hidden simplicity of the gravity action journal, September 2017

Colour-Kinematics duality for one-loop rational amplitudes journal, April 2013

Twofold symmetries of the pure gravity action journal, January 2017

Minimal Basis for Gauge Theory Amplitudes text, January 2009

Monodromy and Jacobi-like Relations for Color-Ordered Amplitudes text, January 2010

The Kinematic Algebra From the Self-Dual Sector text, January 2011

Algebras for Amplitudes text, January 2012

The Structure of n-Point One-Loop Open Superstring Amplitudes text, January 2012

BCJ duality and the double copy in the soft limit text, January 2012

Relationship Between Gravity and Gauge Scattering in the High Energy Limit text, January 2012

Color-Kinematics Duality and the Regge Limit of Inelastic Amplitudes text, January 2012

Colour-Kinematics Duality for One-Loop Rational Amplitudes text, January 2013

Gravity as Gauge Theory Squared: A Ghost Story
journal, November 2018

Black hole in three-dimensional spacetime
journal, September 1992

Einstein's theory in a three-dimensional space-time
journal, August 1984

Geometry of the 2+1 black hole
journal, August 1993

Classical space–times from the S-matrix
journal, December 2013

The double copy: Bremsstrahlung and accelerating black holes
journal, June 2016

New formulas for amplitudes from higher-dimensional operators
journal, February 2017

The classical double copy for Taub–NUT spacetime
journal, November 2015

Transcendence of the Law of Baryon-Number Conservation in Black-Hole Physics
journal, February 1972

One-loop four-point amplitudes in pure and matter-coupled $ \mathcal{N}\leq 4 $ supergravity
journal, March 2013

Black holes in the Brans-Dicke: Theory of gravitation
journal, June 1972

Explicit BCJ numerators from pure spinors
journal, July 2011

Extended solutions for the biadjoint scalar field
journal, December 2017

Two-loop four-gluon amplitudes in N = 4 super-Yang-Mills
journal, May 1997

Perturbative gravity from QCD amplitudes
journal, June 1999

Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
text, January 2019

Color-kinematics duality in multi-Regge kinematics and dimensional reduction
journal, October 2013

Scattering Amplitudes and the Conservative Hamiltonian for Binary Systems at Third Post-Minkowskian Order
journal, May 2019

Monodromy and Jacobi-like relations for color-ordered amplitudes
journal, June 2010

The kinematic algebra from the self-dual sector
journal, July 2011

Gravity as the square of Yang–Mills?
journal, September 2015

Next-to-soft corrections to high energy scattering in QCD and gravity
journal, January 2017

Dyson pairs and zero mass black holes
journal, September 1996

Unifying relations for scattering amplitudes
journal, February 2018

Color-kinematics duality for QCD amplitudes
journal, January 2016

Gravity Amplitudes as Generalized Double Copies of Gauge-Theory Amplitudes
journal, May 2017

Algebras for amplitudes
journal, June 2012

Perturbative Quantum Gravity as a Double Copy of Gauge Theory
journal, August 2010

Exact Solutions of Einstein's Field Equations
book, January 2009

Dual identities inside the gluon and the graviton scattering amplitudes
journal, June 2010

On the relationship between Yang-Mills theory and gravity and its implication for ultraviolet divergences
journal, October 1998

String-inspired BCJ numerators for one-loop MHV amplitudes
journal, January 2016

Perturbative spacetimes from Yang-Mills theory
journal, April 2017

Ultraviolet Properties of $N = 4$ Supergravity at Four Loops
journal, December 2013

Factorization properties of soft graviton amplitudes
journal, May 2011

Three-dimensional classical spacetimes
journal, July 1986

Color-kinematics duality and double-copy construction for amplitudes from higher-dimension operators
journal, October 2012

Type D spacetimes and the Weyl double copy
journal, February 2019

Black holes and the double copy
journal, December 2014

Relationship between gravity and gauge scattering in the high energy limit
journal, January 2013

The Kerr-Schild double copy in curved spacetime
journal, December 2017

A relation between tree amplitudes of closed and open strings
journal, May 1986

Dual-color decompositions at one-loop level in Yang-Mills theory
journal, June 2014

Color-kinematics duality and the Regge limit of inelastic amplitudes
journal, April 2013

The classical double copy in maximally symmetric spacetimes
journal, April 2018

Biadjoint wires
journal, January 2019

Spinning BTZ black hole versus Kerr black hole: A closer look
journal, February 1999

Gauge amplitude identities by on-shell recursion relation in S-matrix program
journal, January 2011

N = 4 Yang-Mills and N = 8 supergravity as limits of string theories
journal, May 1982

Exact solutions for the biadjoint scalar field
journal, December 2016

Are all supergravity theories Yang–Mills squared?
journal, September 2018

Minimal Basis for Gauge Theory Amplitudes
journal, October 2009

The self-dual classical double copy, and the Eguchi-Hanson instanton
journal, January 2019

Inelastic black hole scattering from charged scalar amplitudes
journal, March 2018

Two-loop five-point amplitudes of super Yang-Mills and supergravity in pure spinor superspace
journal, October 2015

Chiral squaring
journal, July 2016

All-loop infrared-divergent behavior of most-subleading-color gauge-theory amplitudes
journal, April 2013

Towards one-loop SYM amplitudes from the pure spinor BRST cohomology: Towards one-loop SYM amplitudes from the pure spinor BRST cohomology
journal, January 2015

Integrand oxidation and one-loop colour-dual numerators in $ \mathcal{N}=4 $ gauge theory
journal, July 2013

The structure of n-point one-loop open superstring amplitudes
journal, August 2014

BCJ duality and the double copy in the soft limit
journal, February 2013

Yang-Mills Origin of Gravitational Symmetries
journal, December 2014

Gravitational radiation from color-kinematics duality
journal, November 2018

A double copy for N = 2 $$ \mathcal{N}=2 $$ supergravity: a linearised tale told on-shell
journal, October 2016

Spontaneously broken Yang-Mills-Einstein supergravities as double copies
journal, June 2017

Hidden simplicity of the gravity action
journal, September 2017

Colour-Kinematics duality for one-loop rational amplitudes
journal, April 2013

Twofold symmetries of the pure gravity action
journal, January 2017

Minimal Basis for Gauge Theory Amplitudes
text, January 2009

Monodromy and Jacobi-like Relations for Color-Ordered Amplitudes
text, January 2010

The Kinematic Algebra From the Self-Dual Sector
text, January 2011

Algebras for Amplitudes
text, January 2012

The Structure of n-Point One-Loop Open Superstring Amplitudes
text, January 2012

BCJ duality and the double copy in the soft limit
text, January 2012

Relationship Between Gravity and Gauge Scattering in the High Energy Limit
text, January 2012

Color-Kinematics Duality and the Regge Limit of Inelastic Amplitudes
text, January 2012

Colour-Kinematics Duality for One-Loop Rational Amplitudes
text, January 2013

Integrand Oxidation and One-Loop Colour-Dual Numerators in N=4 Gauge Theory
text, January 2013

Color-Kinematics Duality in Multi-Regge Kinematics and Dimensional Reduction
text, January 2013

Dual-color decompositions at one-loop level in Yang-Mills theory
text, January 2014