Abstract
Using modern amplitude techniques we compute the leading classical and quantum corrections to the gravitational potential between two massive scalars induced by adding cubic terms to Einstein gravity. We then study the scattering of massless scalars, photons and gravitons off a heavy scalar in the presence of the same R3 deformations, and determine the bending angle in the three cases from the non-analytic component of the scattering amplitude. Similarly to the Einstein-Hilbert case, we find that the classical contribution to the bending angle is universal, but unlike that case, universality is preserved also by the first quantum correction. Finally we extend our analysis to include a deformation of the form ΦR2, where Φ is the dilaton, which arises in the low-energy effective action of the bosonic string in addition to the R3 term, and compute its effect on the graviton bending.
Highlights
In this paper we entertain the possibility of adding higher-derivative curvature terms to the Einstein-Hilbert (EH) action that could arise either from string theory or other ultraviolet completions of gravity, and consider their effect on two quantities or relevance: the Newton potential, and the particle bending angle
Using modern amplitude techniques we compute the leading classical and quantum corrections to the gravitational potential between two massive scalars induced by adding cubic terms to Einstein gravity
We study the scattering of massless scalars, photons and gravitons off a heavy scalar in the presence of the same R3 deformations, and determine the bending angle in the three cases from the non-analytic component of the scattering amplitude
Summary
We compute the leading classical and quantum corrections to the Newton potential induced by adding an R3 coupling to the EH action (1.1). We will later be interested in computing the classical and one-loop quantum contributions to the potential arising from a (in this case leading) oneloop computation This is obtained from the appropriately normalised amplitude by means of a Fourier transform in q [7]. We reinstate the overall factor D = (α′/4)2(κ/2), introduce Newton’s constant GN := κ2/(32π), and perform the Fourier transforms using (A.3) and (A.4) This gives our result for the leading classical and quantum corrections to Newton’s potential arising from the addition of an R3 term to Einstein’s gravity: Vcl(r, p). The coupling G3 appears in the low-energy bosonic string effective action quoted later in (3.21) in the form L′ = (−2/κ2)α′ 2(G3/24) For this particular interaction term, going through the standard procedures one arrives at the following corrections to the potential: VL′. We anticipate that there is no contribution to the bending of massless particles from massive scalars in the presence of the G3 coupling, as discussed
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