We revisit the old black hole S-Matrix construction and its new partial wave expansion of 't Hooft. Inspired by old ideas from non-critical string theory & c = 1 Matrix Quantum Mechanics, we reformulate the scattering in terms of a quantum mechanical model -of waves scattering off inverted harmonic oscillator potentials -that exactly reproduces the unitary black hole S-Matrix for all spherical harmonics; each partial wave corresponds to an inverted harmonic oscillator with ground state energy that is shifted relative to the s-wave oscillator. Identifying a connection to 2d string theory allows us to show that there is an exponential degeneracy in how a given total initial energy may be distributed among many partial waves of the 4d black hole.

Semiholography has been proposed as an effective nonperturbative framework which can consistently combine perturbative and nonperturbative effects for theories like QCD. It is postulated that the strongly coupled nonperturbative sector has a holographic dual in the form of a classical gravity theory in the large N limit, and the perturbative fields determine the gravitational boundary conditions. In this work, we pursue a fundamental derivation of this framework particularly showing how perturbative physics by itself can determine the holographic dual of the infrared, and also the interactions between the perturbative and the holographic sectors. We firstly demonstrate that the interactions between the two sectors can be constrained through the existence of a conserved local energy-momentum tensor for the full system up to hard-soft coupling constants. As an illustration, we set up a biholographic toy theory where both the UV and IR sectors are strongly coupled and holographic with distinct classical gravity duals. In this construction, the requirement that an appropriate gluing can cure the singularities (geodetic incompleteness) of the respective geometries leads us to determine the parameters of the IR theory and the hard-soft couplings in terms of those of the UV theory. The high energy scale behavior of the hard-soft couplings is state-independent but their runnings turn out to be state-dependent. We discuss how our approach can be adapted to the construction of the semiholographic framework for QCD.

Quantum gravity is expected to gauge all global symmetries of effective theories, in the ultraviolet. Inspired by this expectation, we explore the consequences of gauging CPT as a quantum boundary condition in phase space. We find that it provides for a natural semiclassical regularisation and discretisation of the continuous spectrum of a quantum Hamiltonian related to the Dilation operator. We observe that the said spectrum is in correspondence with the zeros of the Riemann zeta and Dirichlet beta functions. Following ideas of Berry and Keating, this may help the pursuit of the Riemann hypothesis. It strengthens the proposal that this quantum Hamiltonian captures the near horizon dynamics of the scattering matrix of the Schwarzschild black hole, given the rich chaotic spectrum upon discretisation. It also explains why the spectrum appears to be erratic despite the unitarity of the scattering matrix.

We study scattering on the black hole horizon in a partial wave basis, with an impact parameter of the order of the Schwarzschild radius or less. This resembles the strong gravity regime where quantum gravitational effects appear. The scattering is governed by an infinite number of virtual gravitons exchanged on the horizon. Remarkably, they can all be summed non-perturbatively in ħ and γ ∼ MPl/MBH. These results generalise those obtained from studying gravitational backreaction. Unlike in the eikonal calculations in flat space, the relevant centre of mass energy of the collisions is not necessarily Planckian; instead it is easily satisfied, s » γ2$$ {M}_{\mathrm{Pl}}^2 $$ M Pl 2 , for semi-classical black holes. The calculation lends further support to the scattering matrix approach to quantum black holes, and is a second-quantised generalisation of the same.

We show that there is a remarkable soft limit in quantum gravity where the information paradox is readily resolved due to virtual soft graviton exchange on the black hole horizon. This regime is where collision energies satisfy √ s γM P l (with γ ∼ M P l /M BH ) near the horizon. We call this the black hole eikonal phase, in contrast to its flat space analogue where collisions are trans-Planckian. Hawking's geometric optics approximation neglects gravitational interactions near the horizon, and results in thermal occupation numbers in the Bogoliubov coefficients. We show that these interactions are mediated by graviton exchange in 2 → 2 scattering near the horizon, and explicitly calculate the S-matrix non-perturbatively in M P l /M BH and . This involves a re-summation of infinitely many ladder diagrams near the horizon, all mediated by virtual soft gravitons. The S-matrix turns out to be a pure phase only upon this re-summation. The impact parameter b satisfies L P l b R S , where R S is the Schwarzschild radius; therefore, our results are agnostic of Planckian physics.Our calculation shows that non-renormalisability of gravity is irrelevant for a resolution of the information problem, and is agnostic of any specific ultraviolet completion. In contrast to the flat space eikonal limit, the black hole eikonal phase involves collisions of extremely low energy near the horizon, thereby avoiding firewalls for black holes much larger than Planck size.