Abstract
We establish a connection between the ultra-Planckian scattering amplitudes in field and string theory and unitarization by black hole formation in these scattering processes. Using as a guideline an explicit microscopic theory in which the black hole represents a bound-state of many soft gravitons at the quantum critical point, we were able to identify and compute a set of perturbative amplitudes relevant for black hole formation. These are the tree-level N-graviton scattering S-matrix elements in a kinematical regime (called classicalization limit) where the two incoming ultra-Planckian gravitons produce a large number N of soft gravitons. We compute these amplitudes by using the Kawai–Lewellen–Tye relations, as well as scattering equations and string theory techniques. We discover that this limit reveals the key features of the microscopic corpuscular black hole N-portrait. In particular, the perturbative suppression factor of a N-graviton final state, derived from the amplitude, matches the non-perturbative black hole entropy when N reaches the quantum criticality value, whereas final states with different value of N are either suppressed or excluded by non-perturbative corpuscular physics. Thus we identify the microscopic reason behind the black hole dominance over other final states including non-black hole classical object. In the parameterization of the classicalization limit the scattering equations can be solved exactly allowing us to obtain closed expressions for the high-energy limit of the open and closed superstring tree-level scattering amplitudes for a generic number N of external legs. We demonstrate matching and complementarity between the string theory and field theory in different large-s and large-N regimes.
Highlights
Introduction and summaryThe formulation of a microscopic picture of black hole production in high-energy particle scattering is crucial for understanding the nature of quantum gravity at ultra-Planckian energies.In particular, this issue is central to the idea that gravity is UV-complete in a non-Wilsonian sense [1], based on the concept of classicalization [2].The standard (Wilsonian) approach to UV-completion implies that interactions at higher and higher energies are regulated by integrating-in-weakly-coupled degrees of freedom of shorter and shorter wavelengths
Guided by non-perturbative input from the corpuscular black hole N -portrait, we identify the black hole formation regime as the regime of multi-particle creation, in form of 2 → N graviton scattering amplitudes, with number of soft gravitons in the final state being given by the number of black hole constituents, as suggested by classicalization
Using the microscopic corpuscular picture of black holes as N -graviton self-bound states at a quantum critical point, we provide the missing non-perturbative information that enables us to translate the N -graviton production processes into the black hole formation, both in field and string theory scatterings
Summary
The formulation of a microscopic picture of black hole production in high-energy particle scattering is crucial for understanding the nature of quantum gravity at ultra-Planckian energies. Using the microscopic corpuscular picture of black holes as N -graviton self-bound states at a quantum critical point, we provide the missing non-perturbative information that enables us to translate the N -graviton production processes into the black hole formation, both in field and string theory scatterings. We match the two results and observe that the exponential suppression expected in the semi-classical theory is reproduced by the perturbative 2 → N gravity amplitudes This matching besides of providing an independent information about the multi-graviton amplitudes, confirms that the microscopic origin of the black hole dominance, relative to other possible multi-particle final states of the same energy, lies in the quantum criticality of the black hole constituents, which is absent for other classical objects. In order to do it we shall briefly review the non-perturbative input coming from the corpuscular black hole portrait, which being a microscopic quantum theory, provides a crucial missing link between the perturbative N -graviton production amplitudes and the unitarization of the theory by black hole formation
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