Evanescent Effects can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences

Bern, Zvi; Cheung, Clifford; Chi, Huan-Hang; Davies, Scott; Dixon, Lance; Nohle, Josh

doi:10.1103/PhysRevLett.115.211301

Title: Evanescent Effects can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences

Abstract

Evanescent operators such as the Gauss-Bonnet term have vanishing perturbative matrix elements in exactly D = 4 dimensions. Similarly, evanescent fields do not propagate in D = 4; a three-form field is in this class, since it is dual to a cosmological-constant contribution. In this Letter, we show that evanescent operators and fields modify the leading ultraviolet divergence in pure gravity. To analyze the divergence, we compute the two-loop identical-helicity four-graviton amplitude and determine the coefficient of the associated (nonevanescent) R³ counterterm studied long ago by Goroff and Sagnotti. We compare two pairs of theories that are dual in D = 4: gravity coupled to nothing or to three-form matter, and gravity coupled to zero-form or to two-form matter. Duff and van Nieuwenhuizen showed that, curiously, the one-loop trace anomaly—the coefficient of the Gauss-Bonnet operator—changes under p-form duality transformations. In addition, we concur and also find that the leading R³ divergence changes under duality transformations. Nevertheless, in both cases, the physical renormalized two-loop identical-helicity four-graviton amplitude can be chosen to respect duality. In particular, its renormalization-scale dependence is unaltered.

Authors:: Bern, Zvi; Cheung, Clifford; Chi, Huan-Hang; Davies, Scott; Dixon, Lance; Nohle, Josh

Publication Date:: Tue Nov 17 00:00:00 EST 2015

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

Sponsoring Org.:: USDOE Office of Science (SC), High Energy Physics (HEP); Gordon and Betty Moore Foundation (GBMF); National Science Foundation (NSF); Simons Foundation

OSTI Identifier:: 1226183

Alternate Identifier(s):: OSTI ID: 1232660; OSTI ID: 1609082

Grant/Contract Number:: SC0009937; SC0010255; AC02-76SF00515; 776; 1066293

Resource Type:: Published Article

Journal Name:: Physical Review Letters

Additional Journal Information:: Journal Name: Physical Review Letters Journal Volume: 115 Journal Issue: 21; Journal ID: ISSN 0031-9007

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Bern, Zvi, Cheung, Clifford, Chi, Huan-Hang, Davies, Scott, Dixon, Lance, and Nohle, Josh. Evanescent Effects can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences.  United States: N. p., 2015. 
Web.  doi:10.1103/PhysRevLett.115.211301.

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                    Bern, Zvi, Cheung, Clifford, Chi, Huan-Hang, Davies, Scott, Dixon, Lance, & Nohle, Josh. Evanescent Effects can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences.  United States.  https://doi.org/10.1103/PhysRevLett.115.211301

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                    Bern, Zvi, Cheung, Clifford, Chi, Huan-Hang, Davies, Scott, Dixon, Lance, and Nohle, Josh. Tue .  
"Evanescent Effects can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences".  United States.  https://doi.org/10.1103/PhysRevLett.115.211301.

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@article{osti_1226183,

  title        = {Evanescent Effects can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences},

  author       = {Bern, Zvi and Cheung, Clifford and Chi, Huan-Hang and Davies, Scott and Dixon, Lance and Nohle, Josh},

  abstractNote = {Evanescent operators such as the Gauss-Bonnet term have vanishing perturbative matrix elements in exactly D = 4 dimensions. Similarly, evanescent fields do not propagate in D = 4; a three-form field is in this class, since it is dual to a cosmological-constant contribution. In this Letter, we show that evanescent operators and fields modify the leading ultraviolet divergence in pure gravity. To analyze the divergence, we compute the two-loop identical-helicity four-graviton amplitude and determine the coefficient of the associated (nonevanescent) R3 counterterm studied long ago by Goroff and Sagnotti. We compare two pairs of theories that are dual in D = 4: gravity coupled to nothing or to three-form matter, and gravity coupled to zero-form or to two-form matter. Duff and van Nieuwenhuizen showed that, curiously, the one-loop trace anomaly—the coefficient of the Gauss-Bonnet operator—changes under p-form duality transformations. In addition, we concur and also find that the leading R3 divergence changes under duality transformations. Nevertheless, in both cases, the physical renormalized two-loop identical-helicity four-graviton amplitude can be chosen to respect duality. In particular, its renormalization-scale dependence is unaltered.},

  doi          = {10.1103/PhysRevLett.115.211301},

  journal      = {Physical Review Letters},

  number       = 21,

  volume       = 115,

  place        = {United States},

  year         = {Tue Nov 17 00:00:00 EST 2015},

  month        = {Tue Nov 17 00:00:00 EST 2015}

}

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Title: Evanescent Effects can Alter Ultraviolet Divergences in Quantum Gravity without Physical Consequences

Abstract

Citation Formats

Self-Duality and Maximally Helicity Violating QCD Amplitudes journal, March 1997

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

Evanescent operators, scheme dependences and double insertions journal, November 1995

Neutralization of the cosmological constant by membrane creation journal, February 1988

Twenty years of the Weyl anomaly journal, June 1994

The tensor reduction and master integrals of the two-loop massless crossed box with light-like legs journal, July 2000

On the vanishing of evanescent operators journal, March 1991

Curvature squared terms and string theories journal, June 1985

Enhanced ultraviolet cancellations in N = 5 supergravity at four loops journal, November 2014

Energy-momentum tensors, supercurrents, (super)traces, and quantum equivalence journal, December 1984

Gauss-Bonnet coupling constant in classically scale-invariant gravity journal, April 2015

Dynamical neutralization of the cosmological constant journal, September 1987

Conformal anomalies in a general background metric journal, May 1977

Two-Loop Helicity Amplitudes for Gluon-Gluon Scattering in QCD and Supersymmetric Yang-Mills Theory journal, March 2002

Quantum equivalence of dual field theories journal, June 1985

Conformal anomalies and the renormalizability problem in quantum gravity journal, July 1975

QCD nonleading corrections to weak decays in dimensional regularization and 't Hooft-Veltman schemes journal, March 1990

Multi-parton amplitudes in gauge theories journal, February 1991

Renormalizable asymtotically free quantum theory of gravity journal, September 1981

Quantum inequivalence of different field representations journal, July 1980

Massive loop amplitudes from unitarity journal, May 1996

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

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

The ultraviolet behavior of Einstein gravity journal, March 1986

Self-Dual Yang-Mills Theory, Integrability and Multiparton Amplitudes journal, January 1996

Composite anomalies in supergravity journal, July 1985

Renormalizable asymptotically free quantum theory of gravity journal, July 1982

Self-dual Yang-Mills theory and one-loop maximally helicity violating multi-gluon amplitudes journal, January 1997

Analytical results for dimensionally regularized massless on-shell double boxes with arbitrary indices and numerators journal, January 2000

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

Quantization of four-form fluxes and dynamical neutralization of the cosmological constant journal, May 2000

Trace anomaly for gravitons journal, September 1978

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

Two-loop quantum gravity journal, July 1992

Ultraviolet cancellations in half-maximal supergravity as a consequence of the double-copy structure journal, November 2012

Progress in One-Loop qcd Computations journal, December 1996

Equivalence of dimensional reduction and dimensional regularisation journal, March 1994

One-loop n-point gauge theory amplitudes, unitarity and collinear limits journal, August 1994

A two-loop four-gluon helicity amplitude in QCD journal, January 2000

Quantum equivalence of different field representations journal, July 1981

Dimensional reduction applied to QCD at three loops journal, September 2006

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

Path integrals and the indefiniteness of the gravitational action journal, June 1978

Trace anomalies in dimensional regularization journal, September 1974

Renormalizability properties of antisymmetric tensor fields coupled to gravity journal, July 1980

One-loop infinities in dimensionally reduced supergravities journal, April 1984

Infrared Photons and Gravitons journal, October 1965

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

Quantum gravity at two loops journal, October 1985

Eikonal methods applied to gravitational scattering amplitudes journal, May 2011

Self-Duality and Maximally Helicity Violating QCD Amplitudes
journal, March 1997

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

Evanescent operators, scheme dependences and double insertions
journal, November 1995

Neutralization of the cosmological constant by membrane creation
journal, February 1988

Twenty years of the Weyl anomaly
journal, June 1994

The tensor reduction and master integrals of the two-loop massless crossed box with light-like legs
journal, July 2000

On the vanishing of evanescent operators
journal, March 1991

Curvature squared terms and string theories
journal, June 1985

Enhanced ultraviolet cancellations in $N = 5$ supergravity at four loops
journal, November 2014

Energy-momentum tensors, supercurrents, (super)traces, and quantum equivalence
journal, December 1984

Gauss-Bonnet coupling constant in classically scale-invariant gravity
journal, April 2015

Dynamical neutralization of the cosmological constant
journal, September 1987

Conformal anomalies in a general background metric
journal, May 1977

Two-Loop Helicity Amplitudes for Gluon-Gluon Scattering in QCD and Supersymmetric Yang-Mills Theory
journal, March 2002

Quantum equivalence of dual field theories
journal, June 1985

Conformal anomalies and the renormalizability problem in quantum gravity
journal, July 1975

QCD nonleading corrections to weak decays in dimensional regularization and 't Hooft-Veltman schemes
journal, March 1990

Multi-parton amplitudes in gauge theories
journal, February 1991

Renormalizable asymtotically free quantum theory of gravity
journal, September 1981

Quantum inequivalence of different field representations
journal, July 1980

Massive loop amplitudes from unitarity
journal, May 1996

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

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

The ultraviolet behavior of Einstein gravity
journal, March 1986

Self-Dual Yang-Mills Theory, Integrability and Multiparton Amplitudes
journal, January 1996

Composite anomalies in supergravity
journal, July 1985

Renormalizable asymptotically free quantum theory of gravity
journal, July 1982

Self-dual Yang-Mills theory and one-loop maximally helicity violating multi-gluon amplitudes
journal, January 1997

Analytical results for dimensionally regularized massless on-shell double boxes with arbitrary indices and numerators
journal, January 2000

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

Quantization of four-form fluxes and dynamical neutralization of the cosmological constant
journal, May 2000

Trace anomaly for gravitons
journal, September 1978

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

Two-loop quantum gravity
journal, July 1992

Ultraviolet cancellations in half-maximal supergravity as a consequence of the double-copy structure
journal, November 2012

Progress in One-Loop qcd Computations
journal, December 1996

Equivalence of dimensional reduction and dimensional regularisation
journal, March 1994

One-loop n-point gauge theory amplitudes, unitarity and collinear limits
journal, August 1994

A two-loop four-gluon helicity amplitude in QCD
journal, January 2000

Quantum equivalence of different field representations
journal, July 1981

Dimensional reduction applied to QCD at three loops
journal, September 2006

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

Path integrals and the indefiniteness of the gravitational action
journal, June 1978

Trace anomalies in dimensional regularization
journal, September 1974

Renormalizability properties of antisymmetric tensor fields coupled to gravity
journal, July 1980

One-loop infinities in dimensionally reduced supergravities
journal, April 1984

Infrared Photons and Gravitons
journal, October 1965

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

Quantum gravity at two loops
journal, October 1985

Eikonal methods applied to gravitational scattering amplitudes
journal, May 2011