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Register a new userNonuniqueness of scattering amplitudes at special points
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We point out little discussed phenomenon in elementary quantum mechanics. In one-dimensional potential scattering problems, the scattering amplitudes are not uniquely determined at special points in parameter space. We examine a few explicit examples. We also discuss the relation with the pole-skipping phenomena recently found in holographic duality. In the holographic pole-skipping, the retarded Greens functions are not uniquely determined at imaginary Matsubara frequencies. It turns out that this universality comes from the fact that the corresponding potential scattering problem has the angular momentum potential.
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We investigate a new property of retarded Greens functions using AdS/CFT. The Greens functions are not unique at special points in complex momentum space. This arises because there is no unique incoming mode at the horizon and is similar to the pole-skipping phenomenon in holographic chaos. Our examples include the bulk scalar field, the bulk Maxwell vector and scalar modes, and the shear mode of gravitational perturbations. In these examples, the special points are always located at $omega_star = -i(2pi T)$ with appropriate values of complex wave number.
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.
We present an identity satisfied by the kinematic factors of diagrams describing the tree amplitudes of massless gauge theories. This identity is a kinematic analog of the Jacobi identity for color factors. Using this we find new relations between color-ordered partial amplitudes. We discuss applications to multi-loop calculations via the unitarity method. In particular, we illustrate the relations between different contributions to a two-loop four-point QCD amplitude. We also use this identity to reorganize gravity tree amplitudes diagram by diagram, offering new insight into the structure of the KLT relations between gauge and gravity tree amplitudes. This can be used to obtain novel relations similar to the KLT ones. We expect this to be helpful in higher-loop studies of the ultraviolet properties of gravity theories.
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 $D=5$.
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.
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