Five-loop four-point integrand of N=8 supergravity as a generalized double copy

Bern, Zvi; Carrasco, John Joseph; Chen, Wei-Ming; Johansson, Henrik; Roiban, Radu; Zeng, Mao

doi:10.1103/PhysRevD.96.126012

Title: Five-loop four-point integrand of $N = 8$ supergravity as a generalized double copy

Abstract

Here, we use the recently developed generalized double-copy procedure to construct an integrand for the five-loop four-point amplitude of $N = 8$ supergravity. This construction starts from a naive double copy of the previously computed corresponding amplitude of $N = 4$ super-Yang-Mills theory. This is then systematically modified by adding contact terms generated in the context of the method of maximal unitarity cuts. For the simpler generalized cuts, whose corresponding contact terms tend to be the most complicated, we derive a set of formulas relating the contact contributions to the violations of the dual Jacobi identities in the relevant gauge-theory amplitudes. For more complex generalized unitarity cuts, which tend to have simpler contact terms associated with them, we use the method of maximal cuts more directly. The five-loop four-point integrand is a crucial ingredient towards future studies of ultraviolet properties of $N = 8$ supergravity at five loops and beyond. We further propose a nontrivial check of the consistency of the integrand, based on modern approaches for integrating over the loop momenta in the ultraviolet region.

Authors:

Bern, Zvi ^[1]; Carrasco, John Joseph ^[2]; Chen, Wei-Ming ^[1]; Johansson, Henrik ^[3]; Roiban, Radu ^[4]; Zeng, Mao ^[1]

Univ. of California, Los Angeles, CA (United States)
Univ. Paris-Saclay, Gif-sur-Yvette (France)
Uppsala Univ. (Sweden); KTH Royal Inst. of Technology, Stockholm (Sweden)
Pennsylvania State Univ., University Park, PA (United States)

Publication Date:: Wed Dec 20 00:00:00 EST 2017

Research Org.:: Univ. of California, Los Angeles, CA (United States); Univ. of California, Santa Barbara, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP); European Research Council (ERC); Knut and Alice Wallenberg Foundation; Ragnar Söderberg Foundation; National Science Foundation (NSF); Swedish Research Council (SRC)

OSTI Identifier:: 1609071

Alternate Identifier(s):: OSTI ID: 1414329

Grant/Contract Number:: SC0009937; SC0013699; PHY11-25915

Resource Type:: Accepted Manuscript

Journal Name:: Physical Review D

Additional Journal Information:: Journal Volume: 96; Journal Issue: 12; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 79 ASTRONOMY AND ASTROPHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Bern, Zvi, Carrasco, John Joseph, Chen, Wei-Ming, Johansson, Henrik, Roiban, Radu, and Zeng, Mao. Five-loop four-point integrand of N=8 supergravity as a generalized double copy.  United States: N. p., 2017. 
Web.  doi:10.1103/PhysRevD.96.126012.

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                    Bern, Zvi, Carrasco, John Joseph, Chen, Wei-Ming, Johansson, Henrik, Roiban, Radu, & Zeng, Mao. Five-loop four-point integrand of N=8 supergravity as a generalized double copy.  United States.  https://doi.org/10.1103/PhysRevD.96.126012

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                    Bern, Zvi, Carrasco, John Joseph, Chen, Wei-Ming, Johansson, Henrik, Roiban, Radu, and Zeng, Mao. Wed .  
"Five-loop four-point integrand of N=8 supergravity as a generalized double copy".  United States.  https://doi.org/10.1103/PhysRevD.96.126012.  https://www.osti.gov/servlets/purl/1609071.

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@article{osti_1609071,

  title        = {Five-loop four-point integrand of N=8 supergravity as a generalized double copy},

  author       = {Bern, Zvi and Carrasco, John Joseph and Chen, Wei-Ming and Johansson, Henrik and Roiban, Radu and Zeng, Mao},

  abstractNote = {Here, we use the recently developed generalized double-copy procedure to construct an integrand for the five-loop four-point amplitude of N=8 supergravity. This construction starts from a naive double copy of the previously computed corresponding amplitude of N=4 super-Yang-Mills theory. This is then systematically modified by adding contact terms generated in the context of the method of maximal unitarity cuts. For the simpler generalized cuts, whose corresponding contact terms tend to be the most complicated, we derive a set of formulas relating the contact contributions to the violations of the dual Jacobi identities in the relevant gauge-theory amplitudes. For more complex generalized unitarity cuts, which tend to have simpler contact terms associated with them, we use the method of maximal cuts more directly. The five-loop four-point integrand is a crucial ingredient towards future studies of ultraviolet properties of N=8 supergravity at five loops and beyond. We further propose a nontrivial check of the consistency of the integrand, based on modern approaches for integrating over the loop momenta in the ultraviolet region.},

  doi          = {10.1103/PhysRevD.96.126012},

  journal      = {Physical Review D},

  number       = 12,

  volume       = 96,

  place        = {United States},

  year         = {Wed Dec 20 00:00:00 EST 2017},

  month        = {Wed Dec 20 00:00:00 EST 2017}

}

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An Asymptotically Safe Guide to Quantum Gravity and Matter
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Type D Spacetimes and the Weyl Double Copy
text, January 2018

Luna, Andres; Monteiro, Ricardo; Nicholson, Isobel
arXiv
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Positive helicity Einstein-Yang-Mills amplitudes from the Double Copy
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Title: Five-loop four-point integrand of N=8 supergravity as a generalized double copy

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Title: Five-loop four-point integrand of $N = 8$ supergravity as a generalized double copy

Integration-by-parts reductions from unitarity cuts and algebraic geometry
journal, February 2016

Semi-abelian Z-theory: NLSM+ϕ 3 from the open string
journal, August 2017

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

New color decompositions for gauge amplitudes at tree and loop level
journal, April 2000

Multivariate residues and maximal unitarity
journal, December 2013

Complete four-loop four-point amplitude in $N = 4$ super-Yang-Mills theory
journal, December 2010

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

Cancellation of conformal and chiral anomalies in $N \geq 5$ supergravities
journal, February 2017

Explicit formulae for Yang-Mills-Einstein amplitudes from the double copy
journal, July 2017

Explicit solutions of the multi-loop integral recurrence relations and its application
journal, April 1997

Equivalent $D = 3$ Supergravity Amplitudes from Double Copies of Three-Algebra and Two-Algebra Gauge Theories
journal, April 2013

$N \geq 4$ supergravity amplitudes from gauge theory at one loop
journal, November 2011

A proof of the explicit minimal-basis expansion of tree amplitudes in gauge field theory
journal, February 2011

Manifest ultraviolet behavior for the three-loop four-point amplitude of $N = 8$ supergravity
journal, November 2008

Multi-centered N = 2 $$ \mathcal{N}=2 $$ BPS black holes: a double copy description
journal, April 2017

Cuts of Feynman integrals in Baikov representation
conference, July 2018

Complete renormalization of QCD at five loops
text, January 2017

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

Evidence for a nonplanar amplituhedron
journal, June 2016

Integration-by-parts reductions from unitarity cuts and algebraic geometry
conference, October 2016

Two-loop supersymmetric QCD and half-maximal supergravity amplitudes
journal, September 2017

Cuts from residues: the one-loop case
journal, June 2017

BCJ numerators from reduced Pfaffian
journal, April 2017

5 loops in 24/5 dimensions
journal, August 2010

Color-kinematics duality for QCD amplitudes
journal, January 2016

String theory dualities and supergravity divergences
journal, June 2010

Complete renormalization of QCD at five loops
journal, March 2017

The four-loop six-gluon NMHV ratio function
journal, January 2016

On relations between multi-gluon and multi-graviton scattering
journal, August 1988

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

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

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

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

Color-Kinematics Duality and Sudakov Form Factor at Five Loops for $N = 4$ Supersymmetric Yang-Mills Theory
journal, December 2016

The five-loop beta function of Yang-Mills theory with fermions
journal, February 2017

Black holes and the double copy
journal, December 2014

Absence of Three-Loop Four-Point Ultraviolet Divergences in $N = 4$ Supergravity
journal, May 2012

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

Twin supergravities from Yang-Mills theory squared
journal, July 2017

Multigluon cross sections and 5-jet production at hadron colliders
journal, January 1989

BCJ relations from a new symmetry of gauge-theory amplitudes
journal, October 2016

Baikov-Lee representations of cut Feynman integrals
journal, June 2017

The vanishing volume of D = 4 superspace
journal, September 2011

Simplifying multiloop integrands and ultraviolet divergences of gauge theory and gravity amplitudes
journal, May 2012

Color-kinematic duality for form factors
journal, February 2013

Global residues and two-loop hepta-cuts
journal, September 2013

Color-kinematics duality for pure Yang-Mills and gravity at one and two loops
journal, August 2015

Elliptic functions and maximal unitarity
journal, April 2015

The momentum kernel of gauge and gravity theories
journal, January 2011

Multi-loop amplitudes in maximally supersymmetric pure spinor field theory
journal, January 2011

Manifesting color-kinematics duality in the scattering equation formalism
journal, September 2016

New Relations for Three-Dimensional Supersymmetric Scattering Amplitudes
journal, June 2012

Method of calculating renormalization-group functions in the scheme of dimensional regularization
journal, May 1980

Scattering amplitudes in N = 2 $$ \mathcal{N}=2 $$ Maxwell-Einstein and Yang-Mills/Einstein supergravity
journal, January 2015

Bending of Light in Quantum Gravity
journal, February 2015

New relations for gauge-theory amplitudes
journal, October 2008

Prescriptive unitarity
journal, June 2017

Multi-leg one-loop gravity amplitudes from gauge theory
journal, April 1999

Uniqueness of two-loop master contours
journal, October 2012

A simple method for calculating counterterms
journal, May 1985

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

FIRE5: A C++ implementation of Feynman Integral REduction
journal, April 2015

Manifesting enhanced cancellations in supergravity: integrands versus integrals
journal, May 2017

Ultraviolet structure of half-maximal supergravity with matter multiplets at two and three loops
journal, September 2013

Polylogarithms, multiple zeta values and superstring amplitudes
journal, August 2013

Pure gravities via color-kinematics duality for fundamental matter
journal, November 2015

Integration by parts: The algorithm to calculate β-functions in 4 loops
journal, November 1981

On the U(1) duality anomaly and the S-matrix of $ \mathcal{N} $ = 4 supergravity
journal, July 2013

Generalized unitarity and six-dimensional helicity
journal, April 2011

Bootstrapping an NMHV amplitude through three loops
journal, October 2014

$ \mathcal{N} \geqslant {4} $ supergravity amplitudes from gauge theory at two loops
journal, December 2011

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

Maximal unitarity for the four-mass double box
journal, June 2014

Cuts of Feynman Integrals in Baikov representation
journal, April 2017

Ultraviolet Behavior of $N = 8$ Supergravity at Four Loops
journal, August 2009

Bootstrapping a Five-Loop Amplitude Using Steinmann Relations
journal, December 2016

Explicit BCJ numerators from pure spinors
journal, July 2011

Double-copy constructions and unitarity cuts
journal, May 2016

Curvature-squared multiplets, evanescent effects, and the U(1) anomaly in $N = 4$ supergravity
journal, September 2017