John Joseph M. Carrasco

Perturbative Quantum Gravity as a Double Copy of Gauge Theory

In a previous paper we observed that (classical) tree-level gauge-theory amplitudes can be rearranged to display a duality between color and kinematics. Once this is imposed, gravity amplitudes are obtained using two copies of gauge-theory diagram numerators. Here we conjecture that this duality persists to all quantum loop orders and can thus be used to obtain multiloop gravity amplitudes easily from gauge-theory ones. As a nontrivial test, we show that the three-loop four-point amplitude of N=4 super-Yang-Mills theory can be arranged into a form satisfying the duality, and by taking double copies of the diagram numerators we obtain the corresponding amplitude of N=8 supergravity. We also remark on a nonsupersymmetric two-loop test based on pure Yang-Mills theory resulting in gravity coupled to an antisymmetric tensor and dilaton.

Ultraviolet Behavior of N ¼ 8 Supergravity at Four Loops

We describe the construction of the complete four-loop four-particle amplitude of N=8 supergravity. The amplitude is ultraviolet finite, not only in four dimensions, but in five dimensions as well. The observed extra cancellations provide additional nontrivial evidence that N=8 supergravity in four dimensions may be ultraviolet finite to all orders of perturbation theory.

Maximally supersymmetric planar Yang-Mills amplitudes at five loops

We present an Ansatz for the planar five-loop four-point amplitude in maximally supersymmetric Yang-Mills theory in terms of loop integrals. This Ansatz exploits the recently observed correspondence between integrals with simple conformal properties and those found in the four-point amplitudes of the theory through four loops. We explain how to identify all such integrals systematically. We make use of generalized unitarity in both four and D dimensions to determine the coefficients of each of these integrals in the amplitude. Maximal cuts, in which we cut all propagators of a given integral, are an especially effective means for determining these coefficients. The set of integrals and coefficients determined here will be useful for computing the five-loop cusp anomalous dimension of the theory which is of interest for nontrivial checks of the AdS/CFT duality conjecture. It will also be useful for checking a conjecture that the amplitudes have an iterative structure allowing for their all-loop resummation, whose link to a recent string-side computation by Alday and Maldacena opens a new venue for quantitative AdS/CFT comparisons.

Manifest Ultraviolet Behavior for the Three-Loop Four-Point Amplitude of N=8 Supergravity

Using the method of maximal cuts, we obtain a form of the three-loop four-point scattering amplitude of

The Effective Field Theory of Cosmological Large Scale Structures

\mathcal{N}=8

Simplifying multiloop integrands and ultraviolet divergences of gauge theory and gravity amplitudes

supergravity in which all ultraviolet cancellations are made manifest. The Feynman loop integrals that appear have a graphical representation with only cubic vertices, and numerator factors that are quadratic in the loop momenta, rather than quartic as in the previous form. This quadratic behavior reflects cancellations beyond those required for finiteness, and matches the quadratic behavior of the three-loop four-point scattering amplitude in

Five-Point Amplitudes in N=4 Super-Yang-Mills Theory and N=8 Supergravity

\mathcal{N}=4

The Complete Four-Loop Four-Point Amplitude in N = 4 Super-Yang-Mills Theory

super-Yang-Mills theory. By direct integration we confirm that no additional cancellations remain in the

One-loop four-point amplitudes in pure and matter-coupled N <= 4 supergravity

\mathcal{N}=8

D = 5 maximally supersymmetric Yang-Mills theory diverges at six loops

supergravity amplitude, thus demonstrating that the critical dimension in which the first ultraviolet divergence occurs at three loops is