No Arabic abstract
Amplitude methods have proven to be a promising technique to perform Post-Minkowskian calculations used as inputs to construct gravitational waveforms. In this paper, we show how these methods can be extended beyond the standard calculations in General Relativity with a minimal coupling to matter. As proof of principle, we consider spinless particles conformally coupled to a gravitational helicity-0 mode. We clarify the subtleties in the matching procedure that lead to the potential for conformally coupled matter. We show that in the probe particle limit, we can reproduce well known results for the field profile. With the scattering amplitudes at hand, we compute the conservative potential and scattering angle for the binary system. We find that the result is a non trivial expansion that involves not only the coupling strengths, but also a non trivial dependence on the energy/momentum of the scattered particles.
We study the renormalization group of generic effective field theories that include gravity. We follow the on-shell amplitude approach, which provides a simple and efficient method to extract anomalous dimensions avoiding complications from gauge redundancies. As an invaluable tool we introduce a modified helicity $tilde{h}$ under which gravitons carry one unit instead of two. With this modified helicity we easily explain old and uncover new non-renormalization theorems for theories including gravitons. We provide complete results for the one-loop gravitational renormalization of a generic minimally coupled gauge theory with scalars and fermions and all orders in $M_{Pl}$, as well as for the renormalization of dimension-six operators including at least one graviton, all up to four external particles.
We present a general framework with which the Schwarzschild-Tangherlini metric of a point particle in arbitrary dimensions can be derived from a scattering amplitude to all orders in the gravitational constant, $G_N$, in covariant gauge (i.e. $R_xi$-gauge) with a generalized de Donder-type gauge function, $G_sigma$. The metric is independent of the covariant gauge parameter $xi$ and obeys the classical gauge condition $G_sigma=0$. We compute the metric with the generalized gauge choice explicitly to second order in $G_N$ where gravitational self-interactions become important and these results verify the general framework to one-loop order. Interestingly, after generalizing to arbitrary dimension, a logarithmic dependence on the radial coordinate appears in space-time dimension $D=5$.
We describe a new perturbation theory for General Relativity, with the chiral first-order Einstein-Cartan action as the starting point. Our main result is a new gauge-fixing procedure that eliminates the connection-to-connection propagator. All other known first-order formalisms have this propagator non-zero, which significantly increases the combinatorial complexity of any perturbative calculation. In contrast, in the absence of the connection-to-connection propagator, our formalism leads to an effective description in which only the metric (or tetrad) propagates, there are only cubic and quartic vertices, but some vertex legs are special in that they cannot be connected by the propagator. The new formalism is the gravity analog of the well-known and powerful chiral description of Yang-Mills theory.
We present the analytic form of the two-loop four-graviton scattering amplitudes in Einstein gravity. To remove ultraviolet divergences we include counterterms quadratic and cubic in the Riemann curvature tensor. The two-loop numerical unitarity approach is used to deal with the challenging momentum dependence of the interactions. We exploit the algebraic properties of the integrand of the amplitude in order to map it to a minimal basis of Feynman integrals. Analytic expressions are obtained from numerical evaluations of the amplitude. Finally, we show that four-graviton scattering observables depend on fewer couplings than naively expected.
The extended-BMS algebra of asymptotically flat spacetime contains an SO(3,1) subgroup that acts by conformal transformations on the celestial sphere. It is of interest to study the representations of this subgroup associated with gravitons. To reduce the equation of motion to a Schrodinger-like equation it is necessary to impose a non-covariant gauge condition. Using these solutions, leading-order gauge invariant Weyl scalars are then computed and decomposed into families of unitary principal series representations. An invertible holographic mapping is constructed between these unitary principal series operators and massless spin-2 perturbations of flat spacetime.