Superstring one-loop and gravitino contributions to planckian scattering

131

We extract the long-range gravitational potential between two scalar particles with arbitrary masses from the two-to-two elastic scattering amplitude at 2nd Post-Minkowskian order in arbitrary dimensions. In contrast to the four-dimensional case, in higher dimensions the classical potential receives contributions from box topologies. Moreover, the kinematical relation between momentum and position on the classical trajectory contains a new term which is quadratic in the tree-level amplitude. A precise interplay between this new relation and the formula for the scattering angle ensures that the latter is still linear in the classical part of the scattering amplitude, to this order, matching an earlier calculation in the eikonal approach. We point out that both the eikonal exponentiation and the reality of the potential to 2nd post-Minkowskian order can be seen as a consequence of unitarity. We finally present closed-form expressions for the scattering angle given by leading-order gravitational potentials for dimensions ranging from four to ten.

Section: Introductionmentioning

confidence: 99%

Second-order post-Minkowskian scattering in arbitrary dimensions

Cristofoli

Damgaard

Vecchia

et al. 2020

131

“…While the classical approach goes back to the seventies [11][12][13], the quantum approach began in the late eighties with the above mentioned work by 't Hooft [10] and independent parallel work by two other groups [14][15][16] dealing with the transplanckian energy collisions of strings in a generic number D of macroscopic spacetime dimensions. That approach was further developed in a number of papers [17][18][19][20][21][22][23][24][25] and extended to the scattering of strings off a stack of D-branes [26,27]. Many features of CGR, such as deflection angles, time delays and tidal excitations, were neatly recovered and new effects related to the finite string size were uncovered [28,29](see [30] for a recent review).…”

Section: Introductionmentioning

confidence: 99%

“…We have been informed by Parra-Martinez that it has also been checked at this subleading level for 4 ≤ N ≤ 8. A first hint for such universality goes back to[20].…”

mentioning

confidence: 99%

A tale of two exponentiations in $$ \mathcal{N} $$ = 8 supergravity at subleading level

Vecchia

Naculich

Russo

et al. 2020

High-energy massless gravitational scattering in N = 8 supergravity was recently analyzed at leading level in the deflection angle, uncovering an interesting connection between exponentiation of infrared divergences in momentum space and the eikonal exponentiation in impact parameter space. Here we extend that analysis to the first non trivial sub-leading level in the deflection angle which, for massless external particles, implies going to two loops, i.e. to third post-Minkowskian (3PM) order. As in the case of the leading eikonal, we see that the factorisation of the momentum space amplitude into the exponential of the one-loop result times a finite remainder hides some basic simplicity of the impact parameter formulation. For the conservative part of the process, the explicit outcome is infrared (IR) finite, shows no logarithmic enhancement, and agrees with an old claim in pure Einstein gravity, while the dissipative part is IR divergent and should be regularized, as usual, by including soft gravitational bremsstrahlung. Finally, using recent three-loop results, we test the expectation that eikonal formulation accounts for the exponentiation of the lower-loop results in the momentum space amplitude. This passes a number of highly non-trivial tests, but appears to fail for the dissipative part of the process at all loop orders and sufficiently subleading order in , hinting at some lack of commutativity of the relevant infrared limits for each exponentiation.

“…For further work on string theory in the Regge limit see[73][74][75][76][77][78][79][80][81][82][83] 30. This is also reviewed in[62] where they showed the connection to commutativity of shockwaves.…”

mentioning

confidence: 99%

AdS/CFT unitarity at higher loops: high-energy string scattering

Meltzer

2020

What is the space of weakly-coupled, gravitational theories which contain massive, higher-spin particles? This class of theories is highly constrained and it is conjectured their ultraviolet completion must be string theory. We provide more evidence for this conjecture by studying the Regge limit in large N , 4d CFTs with single-trace operators of unbounded spin. We show that in the Regge limit, these theories have bulk scattering amplitudes which are consistent with the string theory prediction to all orders in 1/N for large, but finite, coupling. In the language of Regge theory, we show Pomeron exchange naturally exponentiates in the 1/N expansion. To do this, we solve the bootstrap equations at tree-level and then use the Lorentzian inversion formula to find the one-loop correlator in the Regge limit. This is a unitarity method for AdS/CFT which can be repeated iteratively to make all orders statements. We also explain under what conditions the tree-level result exponentiates in the 1/N expansion at arbitrary coupling. Finally, we comment on further inelastic effects and show they give subleading contributions at large coupling. As a consistency check, we recover results from bulk Einstein gravity in the limit where all higher-spin particles decouple.