Finite Quantum Gravity

We hereby present a class of multidimensional higher derivative theories of gravity that realizes an ultraviolet completion of Einstein general relativity. This class is marked by a "non-polynomal" entire function (form factor), which averts extra degrees of freedom (including ghosts) and improves the high energy behavior of the loop amplitudes. By power counting arguments, it is proved that the theory is super-renormalizable in any dimension, i.e. only one-loop divergences survive. Furthermore, in odd dimensions there are no counter terms for pure gravity and the theory turns out to be "finite." Finally, considering the infinite tower of massive states coming from dimensional reduction, quantum gravity is finite in even dimension as well.Comment: 19 pages. arXiv admin note: substantial text overlap with arXiv:1202.315

Massive Nonplanar Two-Loop Maximal Unitarity

We explore maximal unitarity for nonplanar two-loop integrals with up to four massive external legs. In this framework, the amplitude is reduced to a basis of master integrals whose coefficients are extracted from maximal cuts. The hepta-cut of the nonplanar double box defines a nodal algebraic curve associated with a multiply pinched genus-3 Riemann surface. All possible configurations of external masses are covered by two distinct topological pictures in which the curve decomposes into either six or eight Riemann spheres. The procedure relies on consistency equations based on vanishing of integrals of total derivatives and Levi-Civita contractions. Our analysis indicates that these constraints are governed by the global structure of the maximal cut. Lastly, we present an algorithm for computing generalized cuts of massive integrals with higher powers of propagators based on the Bezoutian matrix method.Comment: 54 pages, 9 figures, v2: journal versio

SecDec-3.0: numerical evaluation of multi-scale integrals beyond one loop

SecDec is a program which can be used for the factorization of dimensionally regulated poles from parametric integrals, in particular multi-loop integrals, and the subsequent numerical evaluation of the finite coefficients. Here we present version 3.0 of the program, which has major improvements compared to version 2: it is faster, contains new decomposition strategies, an improved user interface and various other new features which extend the range of applicability.Comment: 46 pages, version to appear in Comput.Phys.Com