Tree-level scattering amplitudes in nonlocal field theories

We review some recent developments in the understanding of field theories in the perturbative regime. In particular, we discuss the notions of analyticity, unitarity and locality, and therefore the singularity structure of scattering amplitudes in general interacting theories. We describe their tree-level structure and their on-shell representations, as well as the links between the tree-level structure itself and the structure of the loop amplitudes. Finally, we describe the...

We investigate features of perturbative gravity and supergravity by studying scattering in the ultraplanckian limit, and sharpen arguments that the dynamics is governed by long-distance physics. A simple example capturing aspects of the eikonal resummation suggests why short distance phenomena and in particular divergences or nonrenormalizability do not necessarily play a central role in this regime. A more profound problem is apparently unitarity. These considerations can be...

We argue that quantum gravity is nonlocal, first by recalling well-known arguments that support this idea and then by focusing on a point not usually emphasized: that making a conventional effective field theory (EFT) for quantum gravity is particularly difficult, and perhaps impossible in principle. This inability to realize an EFT comes down to the fact that gravity itself sets length scales for a problem: when integrating out degrees of freedom above some cutoff, the effec...

Ever since the appearance of renormalization theory there have been several differently motivated attempts at non-localized (in the sense of not generated by point-like fields) relativistic particle theories, the most recent one being at QFT on non-commutative Minkowski spacetime. The often conceptually uncritical and historically forgetful contemporary approach to these problems calls for a critical review the light of previous results on this subject.

It's widely recognized that general relativity emerges if we impose invariance under local translations and local Lorentz transformations. In the same manner supergravity arises when we impose invariance under local supersymmetry. In this paper we show how to treat general relativity as a common gauge theory, without introducing a metric or a tetrad field. The price to pay for such simplification is the acceptance of non-locality. At first glance the resulting theory seems re...

This is a personal recollection of several results related to the study of the high energy limit of scattering amplitudes in gravitational theories. They would not have been possible without the encouragement and constant support from Lev Nikolaevich Lipatov.

We derive new amplitudes relations revealing a hidden unity among wide-ranging theories in arbitrary spacetime dimensions. Our results rely on a set of Lorentz invariant differential operators which transmute physical tree-level scattering amplitudes into new ones. By transmuting the amplitudes of gravity coupled to a dilaton and two-form, we generate all the amplitudes of Einstein-Yang-Mills theory, Dirac-Born-Infield theory, special Galileon, nonlinear sigma model, and biad...

We suggest that classicalization can cure non-local quantum field theories from acausal divergences in scattering amplitudes, restoring unitarity and causality. In particular, in "trans-non-local" limit, the formation of non-perturbative classical configurations, called {\it classicalons}, in scatterings like $\phi\phi\rightarrow \phi\phi$, can avoid typical acausal divergences.

Gauge theory amplitudes in a non-helicity format are generated at all $n$-point and at tree level. These amplitudes inherit structure from $\phi^3$ classical scattering, and the string inspired formalism is used to find the tensor algebra. All of the classical gravity amplitudes are also given. The classical effective action can also be constructed. Generalizations to amplitudes with non spin-1 or 2 is possible.

Recently, tree-level recursion relations for scattering amplitudes of gluons in Yang-Mills theory have been derived. In this note we propose a generalization of the recursion relations to tree-level scattering amplitudes of gravitons. We use the relations to derive new simple formulae for all amplitudes up to six gravitons. In particular, we present an explicit formula for the six graviton non-MHV amplitude. We prove the relations for MHV and next-to-MHV n-graviton amplitudes...