Ultraviolet properties of N=8 supergravity at five loops

Bern, Zvi; Carrasco, John Joseph; Chen, Wei-Ming; Edison, Alex; Johansson, Henrik; Parra-Martinez, Julio; Roiban, Radu; Zeng, Mao

doi:10.1103/PhysRevD.98.086021

Title: Ultraviolet properties of $N = 8$ supergravity at five loops

Abstract

We use the recently developed generalized double-copy construction to obtain an improved representation of the five-loop four-point integrand of $N = 8$ supergravity whose leading ultraviolet behavior we analyze using state-of-the-art loop-integral expansion and reduction methods. We find that the five-loop critical dimension where ultraviolet divergences first occur is $D_{c} = 24 / 5$ , corresponding to a $D^{8} R^{4}$ counterterm. This ultraviolet behavior stands in contrast to the cases of four-dimensional $N = 4$ supergravity at three loops and $N = 5$ supergravity at four loops whose improved ultraviolet behavior demonstrates enhanced cancellations beyond implications from standard symmetry considerations. We express this $D_{c} = 24 / 5$ divergence in terms of two relatively simple positive-definite integrals with vanishing external momenta, excluding any additional ultraviolet cancellations at this loop order. We note nontrivial relations between the integrals describing this leading ultraviolet behavior and integrals describing lower-loop behavior. This observation suggests not only a path towards greatly simplifying future calculations at higher loops, but may even allow us to directly investigate ultraviolet behavior in terms of simplified integrals, avoiding the construction of complete integrands.

Authors:: Bern, Zvi; Carrasco, John Joseph; Chen, Wei-Ming; Edison, Alex; Johansson, Henrik; Parra-Martinez, Julio; Roiban, Radu; Zeng, Mao

Publication Date:: Mon Oct 01 00:00:00 EDT 2018

Research Org.:: Univ. of California, Los Angeles, CA (United States); Pennsylvania State Univ., University Park, PA (United States)

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

OSTI Identifier:: 1478607

Alternate Identifier(s):: OSTI ID: 1608965

Grant/Contract Number:: SC0009937; SC0013699; PHY11-25915; ERC-STG-639729

Resource Type:: Published Article

Journal Name:: Physical Review D

Additional Journal Information:: Journal Name: Physical Review D Journal Volume: 98 Journal Issue: 8; Journal ID: ISSN 2470-0010

Publisher:: American Physical Society (APS)

Country of Publication:: United States

Language:: English

Subject:: 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS

Citation Formats


                    Bern, Zvi, Carrasco, John Joseph, Chen, Wei-Ming, Edison, Alex, Johansson, Henrik, Parra-Martinez, Julio, Roiban, Radu, and Zeng, Mao. Ultraviolet properties of N=8 supergravity at five loops.  United States: N. p., 2018. 
Web.  doi:10.1103/PhysRevD.98.086021.

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                    Bern, Zvi, Carrasco, John Joseph, Chen, Wei-Ming, Edison, Alex, Johansson, Henrik, Parra-Martinez, Julio, Roiban, Radu, & Zeng, Mao. Ultraviolet properties of N=8 supergravity at five loops.  United States.  https://doi.org/10.1103/PhysRevD.98.086021

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                    Bern, Zvi, Carrasco, John Joseph, Chen, Wei-Ming, Edison, Alex, Johansson, Henrik, Parra-Martinez, Julio, Roiban, Radu, and Zeng, Mao. Mon .  
"Ultraviolet properties of N=8 supergravity at five loops".  United States.  https://doi.org/10.1103/PhysRevD.98.086021.

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@article{osti_1478607,

  title        = {Ultraviolet properties of N=8 supergravity at five loops},

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

  abstractNote = {We use the recently developed generalized double-copy construction to obtain an improved representation of the five-loop four-point integrand of N=8 supergravity whose leading ultraviolet behavior we analyze using state-of-the-art loop-integral expansion and reduction methods. We find that the five-loop critical dimension where ultraviolet divergences first occur is Dc=24/5, corresponding to a D8R4 counterterm. This ultraviolet behavior stands in contrast to the cases of four-dimensional N=4 supergravity at three loops and N=5 supergravity at four loops whose improved ultraviolet behavior demonstrates enhanced cancellations beyond implications from standard symmetry considerations. We express this Dc=24/5 divergence in terms of two relatively simple positive-definite integrals with vanishing external momenta, excluding any additional ultraviolet cancellations at this loop order. We note nontrivial relations between the integrals describing this leading ultraviolet behavior and integrals describing lower-loop behavior. This observation suggests not only a path towards greatly simplifying future calculations at higher loops, but may even allow us to directly investigate ultraviolet behavior in terms of simplified integrals, avoiding the construction of complete integrands.},

  doi          = {10.1103/PhysRevD.98.086021},

  journal      = {Physical Review D},

  number       = 8,

  volume       = 98,

  place        = {United States},

  year         = {Mon Oct 01 00:00:00 EDT 2018},

  month        = {Mon Oct 01 00:00:00 EDT 2018}

}

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