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Cancellations beyond finiteness in N=8 supergravity at three loops.

Z Bern¹, J J Carrasco, L J Dixon

¹Department of Physics and Astronomy, UCLA, Los Angeles, California 90095-1547, USA.

Physical Review Letters

|May 16, 2007

Summary

We calculated the three-loop amplitude for N=8 supergravity. Unexpected cancellations suggest N=8 supergravity might be a finite theory of quantum gravity, even at higher loop orders.

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Area of Science:

Theoretical physics
Quantum gravity
String theory

Background:

N=8 supergravity is a candidate theory for quantum gravity.
Understanding its ultraviolet behavior is crucial for its validity.
Previous analyses suggested potential divergences.

Purpose of the Study:

To construct the three-loop four-point amplitude of N=8 supergravity.
To investigate the ultraviolet finiteness of N=8 supergravity.
To explore potential cancellations leading to finiteness.

Main Methods:

Unitarity method for amplitude construction.
Analysis of ultraviolet divergences in D dimensions.
Comparison with N=4 super-Yang-Mills theory.

Main Results:

The three-loop four-point amplitude of N=8 supergravity was constructed.
The amplitude exhibits ultraviolet finiteness in four dimensions.
Novel cancellations were identified, improving the divergence degree in D dimensions.

Conclusions:

N=8 supergravity exhibits unexpected cancellations.
These cancellations suggest N=8 supergravity may be a perturbatively finite theory of quantum gravity.
Finiteness extends to higher loop orders, indicated by unitarity cuts.