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Register a new userFour-graviton scattering to three loops in ${mathcal N}=8$ supergravity
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We compute the three-loop scattering amplitude of four gravitons in ${mathcal N}=8$ supergravity. Our results are analytic formulae for a Laurent expansion of the amplitude in the regulator of dimensional regularisation. The coefficients of this series are closed formulae in terms of well-established harmonic poly-logarithms. Our results display a remarkable degree of simplicity and represent an important stepping stone in the exploration of the structure of scattering amplitudes. In particular, we observe that to this loop order the four graviton amplitude is given by uniform weight $2L$ functions, where $L$ is the loop order.
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We compute the three-loop four-gluon scattering amplitude in maximally supersymmetric Yang-Mills theory, including its full color dependence. Our result is the first complete computation of a non-planar four-particle scattering amplitude to three loops in four-dimensional gauge theory and consequently provides highly non-trivial data for the study of non-planar scattering amplitudes. We present the amplitude as a Laurent expansion in the dimensional regulator to finite order, with coefficients composed of harmonic poly-logarithms of uniform transcendental weight, and simple rational prefactors. Our computation provides an independent check of a recent result for three-loop corrections to the soft anomalous dimension matrix that predicts the general infrared singularity structure of massless gauge theory scattering amplitudes. Taking the Regge limit of our result, we determine the three-loop gluon Regge trajectory. We also find agreement with very recent predictions for sub-leading logarithms.
Using the method of maximal cuts, we obtain a form of the three-loop four-point scattering amplitude of N=8 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 N=4 super-Yang-Mills theory. By direct integration we confirm that no additional cancellations remain in the N=8 supergravity amplitude, thus demonstrating that the critical dimension in which the first ultraviolet divergence occurs at three loops is D_c=6. We also give the values of the three-loop divergences in D=7,9,11. In addition, we present the explicitly color-dressed three-loop four-point amplitude of N=4 super-Yang-Mills theory.
We present numerical results for the nonplanar lightlike cusp and collinear anomalous dimension at four loops in ${mathcal N} = 4$ SYM theory, which we infer from a calculation of the Sudakov form factor. The latter is expressed as a rational linear combination of uniformly transcendental integrals for arbitrary colour factor. Numerical integration in the nonplanar sector reveals explicitly the breakdown of quadratic Casimir scaling at the four-loop order. A thorough analysis of the reported numerical uncertainties is carried out.
We give a classification of fully supersymmetric chiral ${cal N}=(8,0)$ AdS$_3$ vacua in general three-dimensional half-maximal gauged supergravities coupled to matter. These theories exhibit a wealth of supersymmetric vacua with background isometries given by the supergroups OSp$(8|2,mathbb{R})$, F(4), SU$(4|1,1)$, and OSp$(4^*|4)$, respectively. We identify the associated embedding tensors and the structure of the associated gauge groups. We furthermore compute the mass spectra around these vacua. As an off-spin we include results for a number of ${cal N}=(7,0)$ vacua with supergroups OSp$(7|2,mathbb{R})$ and G$(3)$, respectively. We also comment on their possible higher-dimensional uplifts.
Candidate counterterms break Noether-Gaillard-Zumino E_{7(7)} current conservation in N=8 supergravity in four dimensions. Bossard and Nicolai proposed a scheme for deforming the subsector involving vector fields in a Lorentz covariant manner, so as to restore duality. They argued that there must exist an extension of this deformation to the full theory that preserves supersymmetry. We show that it is not possible to deform the maximal supergravity to restore E_{7(7)} duality, while maintaining both general covariance and N=8 supersymmetry, as was proposed. Deformation of N=8 supergravity requires higher spins and multiple gravitons, which presents a concrete obstacle to this proposal.
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