UV cancellations in gravity loop integrands

Herrmann, Enrico; Trnka, Jaroslav

doi:10.1007/jhep02(2019)084

Title: UV cancellations in gravity loop integrands

Abstract

In this work we explore the properties of four-dimensional gravity integrands at large loop momenta. This analysis can not be done directly for the full off-shell integrand but only becomes well-defined on cuts that allow us to unambiguously specify labels for the loop variables. The ultraviolet region of scattering amplitudes originates from poles at infinity of the loop integrands and we show that in gravity these integrands conceal a number of surprising features. In particular, certain poles at infinity are absent which requires a conspiracy between individual Feynman integrals contributing to the amplitude. We suspect that this non-trivial behavior is a consequence of yet-to-be found symmetry or a hidden property of gravity amplitudes.

Authors:

^[1]; Trnka, Jaroslav ^[2]

Stanford Univ., Stanford, CA (United States)
Univ. of California, Davis, CA (United States)

Publication Date:: Thu Feb 14 00:00:00 EST 2019

Research Org.:: SLAC National Accelerator Laboratory (SLAC), Menlo Park, CA (United States); Univ. of California, Davis, CA (United States)

Sponsoring Org.:: USDOE Office of Science (SC)

OSTI Identifier:: 1506959

Alternate Identifier(s):: OSTI ID: 1600537

Grant/Contract Number:: AC02-76SF00515; SC0009999

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: 2; Journal ID: ISSN 1029-8479

Publisher:: Springer Berlin

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; Scattering Amplitudes; Extended Supersymmetry; Supergravity Models

Citation Formats


                    Herrmann, Enrico, and Trnka, Jaroslav. UV cancellations in gravity loop integrands.  United States: N. p., 2019. 
Web.  doi:10.1007/jhep02(2019)084.

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                    Herrmann, Enrico, & Trnka, Jaroslav. UV cancellations in gravity loop integrands.  United States.  https://doi.org/10.1007/jhep02(2019)084

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                    Herrmann, Enrico, and Trnka, Jaroslav. Thu .  
"UV cancellations in gravity loop integrands".  United States.  https://doi.org/10.1007/jhep02(2019)084.  https://www.osti.gov/servlets/purl/1506959.

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@article{osti_1506959,

  title        = {UV cancellations in gravity loop integrands},

  author       = {Herrmann, Enrico and Trnka, Jaroslav},

  abstractNote = {In this work we explore the properties of four-dimensional gravity integrands at large loop momenta. This analysis can not be done directly for the full off-shell integrand but only becomes well-defined on cuts that allow us to unambiguously specify labels for the loop variables. The ultraviolet region of scattering amplitudes originates from poles at infinity of the loop integrands and we show that in gravity these integrands conceal a number of surprising features. In particular, certain poles at infinity are absent which requires a conspiracy between individual Feynman integrals contributing to the amplitude. We suspect that this non-trivial behavior is a consequence of yet-to-be found symmetry or a hidden property of gravity amplitudes.},

  doi          = {10.1007/jhep02(2019)084},

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

  number       = 2,

  volume       = 2019,

  place        = {United States},

  year         = {Thu Feb 14 00:00:00 EST 2019},

  month        = {Thu Feb 14 00:00:00 EST 2019}

}

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Works referencing / citing this record:

The two-loop five-particle amplitude in $\mathcal{N}=8$ supergravity
text, January 2019

Chicherin, D.; Gehrmann, T.; Henn, J. M.
arXiv
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The two-loop five-point amplitude in $\mathcal N=8$ supergravity
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Title: UV cancellations in gravity loop integrands

Abstract

Citation Formats

Singularity Structure of Maximally Supersymmetric Scattering Amplitudes journal, December 2014

d-dimensional unitarity cut method journal, February 2007

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

Dual Conformal Structure Beyond the Planar Limit journal, September 2018

The Amplituhedron journal, October 2014

Integration by Parts: an Introduction journal, July 2011

Evanescent Effects can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences journal, November 2015

Two-loop scattering amplitudes from the Riemann sphere journal, December 2016

Biadjoint scalar tree amplitudes and intersecting dual associahedra text, January 2018

Grassmannian Geometry of Scattering Amplitudes book, May 2016

Local integrand representations of all two-loop amplitudes in planar SYM journal, August 2015

Evidence for a nonplanar amplituhedron journal, June 2016

Properties of scattering forms and their relation to associahedra journal, March 2018

Absence of triangles in maximal supergravity amplitudes journal, October 2008

Unexpected cancellations in gravity theories journal, January 2008

Into the amplituhedron journal, December 2014

Infinities within graviton scattering amplitudes journal, February 1997

Integration by parts: An introduction text, January 2011

One-loop amplitudes on the Riemann sphere text, January 2015

New Representations of the Perturbative S Matrix journal, February 2016

Logarithmic Singularities and Maximally Supersymmetric Amplitudes preprint, January 2014

Factorization in one-loop gauge theory journal, August 1995

Manifesting enhanced cancellations in supergravity: integrands versus integrals text, January 2017

Absence of Triangles in Maximal Supergravity Amplitudes text, January 2008

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

Implications of nonplanar dual conformal symmetry text, January 2018

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

Factorization properties of soft graviton amplitudes journal, May 2011

The tree formula for MHV graviton amplitudes journal, July 2010

The ultraviolet behavior of Einstein gravity journal, March 1986

What is the simplest quantum field theory? journal, September 2010

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

Fusing gauge theory tree amplitudes into loop amplitudes journal, February 1995

The vanishing volume of D=4 superspace text, January 2011

Local Integrand Representations of All Two-Loop Amplitudes in Planar SYM text, January 2015

Soft-collinear gravity journal, September 2012

One-loop n-point helicity amplitudes in (self-dual) gravity journal, December 1998

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

Gravity On-shell Diagrams text, January 2016

Simplicity in the structure of QED and gravity amplitudes journal, February 2009

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

Implications of nonplanar dual conformal symmetry journal, September 2018

Two-loop quantum gravity journal, July 1992

Logarithmic singularities and maximally supersymmetric amplitudes journal, June 2015

Renormalizability Properties of Supergravity text, January 2015

Two-loop graviton scattering relation and IR behavior in supergravity journal, December 2008

The Tree Formula for MHV Graviton Amplitudes text, January 2009

Prescriptive Unitarity text, January 2017

What is the Simplest Quantum Field Theory? text, January 2008

Evidence for a Nonplanar Amplituhedron text, January 2015

Infrared Photons and Gravitons journal, October 1965

Prescriptive unitarity journal, June 2017

Dual conformal symmetry, integration-by-parts reduction, differential equations, and the nonplanar sector journal, November 2017

Renormalizability Properties of Supergravity journal, March 1977

Unwinding the amplituhedron in binary journal, January 2018

Collinear and soft divergences in perturbative quantum gravity journal, November 2011

Unwinding the Amplituhedron in Binary text, January 2017

Scattering forms and the positive geometry of kinematics, color and the worldsheet journal, May 2018

Ultraviolet properties of N = 8 supergravity at five loops journal, October 2018

Five-point amplitudes in N = 4 super-Yang-Mills theory and N = 8 supergravity journal, January 2012

Maximally supersymmetric planar Yang-Mills amplitudes at five loops journal, December 2007

Gravity on-shell diagrams journal, November 2016

Quantum gravity at two loops journal, October 1985

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

Eikonal methods applied to gravitational scattering amplitudes journal, May 2011

Local integrals for planar scattering amplitudes journal, June 2012

5 loops in 24/5 dimensions journal, August 2010

The footprint of E 7(7) in amplitudes of 𝒩 = 8 supergravity journal, January 2009

On-shell diagrams for N $$ \mathcal{N} $$ = 8 supergravity amplitudes journal, June 2016

Regularization and renormalization of gauge fields journal, July 1972

The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM journal, January 2011

Ultraviolet Behavior of $\mathcal{N}\, = \,8$ Supergravity conference, April 2012

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

Integration by parts: An introduction text, January 2011

Two-Loop Scattering Amplitudes from the Riemann Sphere text, January 2016

The two-loop five-particle amplitude in $\mathcal{N}=8$ supergravity text, January 2019

The two-loop five-point amplitude in $\mathcal N=8$ supergravity text, January 2019

Singularity Structure of Maximally Supersymmetric Scattering Amplitudes
journal, December 2014

d-dimensional unitarity cut method
journal, February 2007

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

Dual Conformal Structure Beyond the Planar Limit
journal, September 2018

The Amplituhedron
journal, October 2014

Integration by Parts: an Introduction
journal, July 2011

Evanescent Effects can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences
journal, November 2015

Two-loop scattering amplitudes from the Riemann sphere
journal, December 2016

Biadjoint scalar tree amplitudes and intersecting dual associahedra
text, January 2018

Grassmannian Geometry of Scattering Amplitudes
book, May 2016

Local integrand representations of all two-loop amplitudes in planar SYM
journal, August 2015

Evidence for a nonplanar amplituhedron
journal, June 2016

Properties of scattering forms and their relation to associahedra
journal, March 2018

Absence of triangles in maximal supergravity amplitudes
journal, October 2008

Unexpected cancellations in gravity theories
journal, January 2008

Into the amplituhedron
journal, December 2014

Infinities within graviton scattering amplitudes
journal, February 1997

Integration by parts: An introduction
text, January 2011

One-loop amplitudes on the Riemann sphere
text, January 2015

New Representations of the Perturbative $S$ Matrix
journal, February 2016

Logarithmic Singularities and Maximally Supersymmetric Amplitudes
preprint, January 2014

Factorization in one-loop gauge theory
journal, August 1995

Manifesting enhanced cancellations in supergravity: integrands versus integrals
text, January 2017

Absence of Triangles in Maximal Supergravity Amplitudes
text, January 2008

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

Implications of nonplanar dual conformal symmetry
text, January 2018

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

Factorization properties of soft graviton amplitudes
journal, May 2011

The tree formula for MHV graviton amplitudes
journal, July 2010

The ultraviolet behavior of Einstein gravity
journal, March 1986

What is the simplest quantum field theory?
journal, September 2010

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

Fusing gauge theory tree amplitudes into loop amplitudes
journal, February 1995

The vanishing volume of D=4 superspace
text, January 2011

Local Integrand Representations of All Two-Loop Amplitudes in Planar SYM
text, January 2015

Soft-collinear gravity
journal, September 2012

One-loop n-point helicity amplitudes in (self-dual) gravity
journal, December 1998

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

Gravity On-shell Diagrams
text, January 2016

Simplicity in the structure of QED and gravity amplitudes
journal, February 2009

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

Implications of nonplanar dual conformal symmetry
journal, September 2018

Two-loop quantum gravity
journal, July 1992

Logarithmic singularities and maximally supersymmetric amplitudes
journal, June 2015

Renormalizability Properties of Supergravity
text, January 2015

Two-loop graviton scattering relation and IR behavior in supergravity
journal, December 2008

The Tree Formula for MHV Graviton Amplitudes
text, January 2009

Prescriptive Unitarity
text, January 2017

What is the Simplest Quantum Field Theory?
text, January 2008

Evidence for a Nonplanar Amplituhedron
text, January 2015

Infrared Photons and Gravitons
journal, October 1965

Prescriptive unitarity
journal, June 2017

Dual conformal symmetry, integration-by-parts reduction, differential equations, and the nonplanar sector
journal, November 2017

Renormalizability Properties of Supergravity
journal, March 1977

Unwinding the amplituhedron in binary
journal, January 2018

Collinear and soft divergences in perturbative quantum gravity
journal, November 2011

Unwinding the Amplituhedron in Binary
text, January 2017

Scattering forms and the positive geometry of kinematics, color and the worldsheet
journal, May 2018

Ultraviolet properties of $N = 8$ supergravity at five loops
journal, October 2018

Five-point amplitudes in $N = 4$ super-Yang-Mills theory and $N = 8$ supergravity
journal, January 2012

Maximally supersymmetric planar Yang-Mills amplitudes at five loops
journal, December 2007

Gravity on-shell diagrams
journal, November 2016

Quantum gravity at two loops
journal, October 1985

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

Eikonal methods applied to gravitational scattering amplitudes
journal, May 2011

Local integrals for planar scattering amplitudes
journal, June 2012

5 loops in 24/5 dimensions
journal, August 2010

The footprint of E ₇₍₇₎ in amplitudes of 𝒩 = 8 supergravity
journal, January 2009

On-shell diagrams for N $$ \mathcal{N} $$ = 8 supergravity amplitudes
journal, June 2016

Regularization and renormalization of gauge fields
journal, July 1972

The all-loop integrand for scattering amplitudes in planar $ \mathcal{N} = 4 $ SYM
journal, January 2011

Ultraviolet Behavior of $\mathcal{N}\, = \,8$ Supergravity
conference, April 2012

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

Integration by parts: An introduction
text, January 2011

Two-Loop Scattering Amplitudes from the Riemann Sphere
text, January 2016

The two-loop five-particle amplitude in $\mathcal{N}=8$ supergravity
text, January 2019

The two-loop five-point amplitude in $\mathcal N=8$ supergravity
text, January 2019