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Two-loop n-point anomalous amplitudes in supergravity.

Zvi Bern1, David Kosower2, Julio Parra-Martinez1

  • 1Mani L. Bhaumik Institute for Theoretical Physics, UCLA Department of Physics and Astronomy, Los Angeles, CA 90095, USA.

Proceedings. Mathematical, Physical, and Engineering Sciences
|April 10, 2020
PubMed
Summary
This summary is machine-generated.

Researchers computed two-loop four-point amplitudes in pure supergravity using unitarity and double-copy methods. This work advances understanding of gravitational amplitudes and their finiteness properties in quantum field theory.

Keywords:
S-matrixanomaliesgravityscattering amplitudessupergravity

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Area of Science:

  • Theoretical Physics
  • Quantum Field Theory
  • String Theory

Background:

  • Supergravity theories are extensions of general relativity that include fermionic supersymmetry.
  • Calculating scattering amplitudes in quantum gravity is notoriously challenging, especially at higher loop orders.
  • The double-copy construction provides a powerful method for relating gauge and gravitational theories.

Purpose of the Study:

  • To compute anomalous two-loop four-point amplitudes in N=4 supergravity.
  • To determine previously undetermined terms in all-multiplicity two-loop anomalous superamplitudes.
  • To investigate the role of a proposed finite counterterm in preserving finiteness of amplitudes.

Main Methods:

  • Unitarity methods were employed to construct amplitudes from lower-point processes.
  • The double-copy construction was utilized to relate supergravity amplitudes to gauge theory amplitudes.
  • Four-dimensional cuts were used to isolate specific contributions to the amplitudes.

Main Results:

  • The anomalous two-loop four-point amplitudes in N=4 pure supergravity were computed.
  • All terms determined by four-dimensional cuts in two all-multiplicity two-loop anomalous superamplitudes were presented.
  • The first two-loop n-point gravity amplitude, up to undetermined terms, was determined at four points.
  • A recently proposed finite counterterm was shown to cancel these amplitudes at this order.

Conclusions:

  • The computed amplitudes provide a significant step towards understanding multi-loop scattering in supergravity.
  • The study confirms the effectiveness of unitarity and the double-copy construction for higher-loop calculations.
  • The proposed counterterm is argued to maintain the three-loop finiteness of anomalous amplitudes in N=4 supergravity.