arXiv subjects
Publications and source records attributed to N. E. J. Bjerrum-Bohr.
We formulate new integration rules for one-loop scattering equations analogous to those at tree-level, and test them in a number of non-trivial cases for amplitudes in scalar $ϕ^3$-theory. This formalism greatly facilitates the evaluation of amplitudes in the CHY representation at one-loop order, without the need to explicitly sum over the solutions to the loop-level scattering equations.
We show a direct matching between individual Feynman diagrams and integration measures in the scattering equation formalism of Cachazo, He and Yuan. The connection is most easily explained in terms of triangular graphs associated with planar Feynman diagrams in $ϕ^3$-theory. We also discuss the generalization to general scalar field theories with $ϕ^p$ interactions, corresponding to polygonal graphs involving vertices of order $p$. Finally, we describe how the same graph-theoretic language can be used to provide the precise link between individual Feynman diagrams and string theory integrands.
As described by Cachazo, He and Yuan, scattering amplitudes in many quantum field theories can be represented as integrals that are fully localized on solutions to the so-called scattering equations. Because the number of solutions to the scattering equations grows quite rapidly, the contour of integration involves contributions from many isolated components. In this paper, we provide a simple, combinatorial rule that immediately provides the result of integration against the scattering equation constraints for any Möbius-invariant integrand involving only simple poles. These rules have a simple diagrammatic interpretation that makes the evaluation of any such integrand immediate. Finally, we explain how these rules are related to the computation of amplitudes in the field theory limit of string theory.
We show how modern methods can be applied to quantum gravity at low energy. We test how quantum corrections challenge the classical framework behind the Equivalence Principle, for instance through introduction of non-locality from quantum physics, embodied in the Uncertainty Principle. When the energy is small we now have the tools to address this conflict explicitly. Despite the violation of some classical concepts, the EP continues to provide the core of the quantum gravity framework through the symmetry - general coordinate invariance - that is used to organize the effective field theory.
We use the feature that the gravitational Compton scattering amplitude factorizes in terms of Abelian QED amplitudes to evaluate various gravitational Compton processes. We examine both the QED and gravitational Compton scattering from a massive spin-1 system by the use of helicity amplitude methods. In the case of gravitational Compton scattering we show how the massless limit can be used to evaluate the cross section for graviton-photon scattering and discuss the difference between photon interactions and the zero mass spin-1 limit. We show that the forward scattering cross section for graviton photoproduction has a very peculiar behavior, differing from the standard Thomson and Rutherford cross sections for a Coulomb-like potential.
Tree-level amplitudes of gauge theories are expressed in a basis of auxiliary amplitudes with only cubic vertices. The vertices in this formalism are explicitly factorized in color and kinematics, clarifying the color-kinematics duality in gauge theory amplitudes. The basis is constructed making use of the KK and BCJ relations, thereby showing precisely how these relations underlie the color-kinematics duality. We express gravity amplitudes in terms of a related basis of color-dressed gauge theory amplitudes, with basis coefficients which are permutation symmetric.
We investigate generic properties of one-loop amplitudes in unordered gauge theories in four dimensions. For such theories the organisation of amplitudes in manifestly crossing symmetric expressions poses restrictions on their structure and results in remarkable cancellations. We show that one-loop multi-photon amplitudes in QED with at least eight external photons are given only by scalar box integral functions. This QED `no-triangle' property is true for all helicity configurations and has similarities to the `no-triangle' property found in the case of maximal N = 8 supergravity. Results are derived both via a world-line formalism as well as using on-shell unitarity methods. We show that the simple structure of the loop amplitude originates from the extremely good BCFW scaling behaviour of the QED tree-amplitude.
We investigate the existence of relations for finite one-loop amplitudes in Yang-Mills theory. Using a diagrammatic formalism and a remarkable connection between tree and loop level, we deduce sequences of amplitude relations for any number of external legs.
We discuss a set of recently discovered quadratic relations between gauge theory amplitudes. Such relations give additional structural simplifications for amplitudes in QCD. Remarkably, their origin lie in an analogous set of relations that involve also gravitons. When certain gluon helicities are flipped we obtain relations that do not involve gravitons, but which refer only to QCD.
Using only general features of the S-matrix and quantum field theory, we prove by induction the Kawai-Lewellen-Tye relations that link products of gauge theory amplitudes to gravity amplitudes at tree level. As a bonus of our analysis, we provide a novel and more symmetric form of these relations. We also establish an infinite tower of new identities between amplitudes in gauge theories.
We derive an explicit formula for factorizing an $n$-point closed string amplitude into open string amplitudes. Our results are phrased in terms of a momentum kernel which in the limit of infinite string tension reduces to the corresponding field theory kernel. The same momentum kernel encodes the monodromy relations which lead to the minimal basis of color-ordered amplitudes in Yang-Mills theory. There are interesting consequences of the momentum kernel pertaining to soft limits of amplitudes. We also comment on surprising links between gravity and certain combinations of kinematic and color factors in gauge theory.
Using BCFW on-shell recursion techniques, we prove a sequence of explicit n-point Kawai-Lewellen-Tye relations between gravity and Yang-Mills amplitudes at tree level.
Color-ordered amplitudes in gauge theories satisfy non-linear identities involving amplitude products of different helicity configurations. We consider the origin of such identities and connect them to the Kawai-Lewellen-Tye (KLT) relations between gravity and gauge theory amplitudes. Extensions are made to one-loop order of the full N=4 super Yang-Mills multiplet.
We are still learning intriguing new facets of the string theory motivated Kawai-Lewellen-Tye (KLT) relations linking products of amplitudes in Yang-Mills theories and amplitudes in gravity. This is very clearly displayed in computations of N=8 supergravity where the perturbative expansion show a vast number of similarities to that of N=4 super-Yang-Mills. We will here investigate how identities based on monodromy relations for Yang-Mills amplitudes can be very useful for organizing and further streamlining the KLT relations yielding even more compact results for gravity amplitudes.
We discuss monodromy relations between different color-ordered amplitudes in gauge theories. We show that Jacobi-like relations of Bern, Carrasco and Johansson can be introduced in a manner that is compatible with these monodromy relations. The Jacobi-like relations are not the most general set of equations that satisfy this criterion. Applications to supergravity amplitudes follow straightforwardly through the KLT-relations. We explicitly show how the tree-level relations give rise to non-trivial identities at loop level.
We fabricate gravitino vertex interactions using as only input on-shell Yang-Mills amplitudes and the Kawai-Lewellen-Tye gauge theory / gravity relations. A useful result of this analysis is simpler tree-level Feynman rules for gravitino scattering than in traditional gauges. All results are explicitly verified until five point scattering.
Identities based on monodromy for integrations in string theory are used to derive relations between different color ordered tree-level amplitudes in both bosonic and supersymmetric string theory. These relations imply that the color ordered tree-level n-point gauge theory amplitudes can be expanded in a minimal basis of (n-3)! amplitudes. This result holds for any choice of polarizations of the external states and in any number of dimensions.
From general arguments, we show that one-loop n-point amplitudes in colourless theories satisfy a new type of reduction formula. These lead to the existence of cancellations beyond supersymmetry. Using such reduction relations we prove the no-triangle hypothesis in maximal supergravity by showing that in four dimensions the n-point graviton amplitude contain only scalar box integral functions. We also discuss the reduction formulas in the context of gravity amplitudes with less and no supersymmetry.