After reviewing the role Quasi-Normal Modes (QNMs) play in the Gravitational Wave (GW) signals emitted in the ring-down phase of Black-Hole (BH) mergers, we present a novel efficient approach to compute QNMs of BHs, D-branes and fuzz-balls, based on quantum Seiberg-Witten (SW) curves for N=2 supersymmetric Yang-Mills (SYM) theories. We find remarkable agreement with numerical results obtained by means of Leaver's method of continuous fractions and with `semi-classical' results obtained in the eikonal approximation, based on geodetic motion. Finally we discuss the extension to D3-branes and their bound states of Couch-Torrence (CT) conformal inversions, that exchange horizon and infinity, and show that they keep the photon-sphere (or photon-halo) fixed.

Ultra-planckian collisions represent a fertile arena where to test quantum theories of gravity such as string theory. Glimpses of black hole formation and evaporation can be taken. For suitably defined infrared-safe observables, we show that the `classicalization' approach to high-multiplicity processes agrees with the ACV approach based on the resummation of ladder diagrams. Since a significant fraction of energy is lost in gravitational bremsstrahlung, we re-derived the zero-frequency limit (ZFL) of the GW flux using soft graviton theorems at leading order and compute the corrections at sub- and sub-sub-leading order. For massless two-particle elastic collisions the former is shown to vanish, while the latter takes an explicit expression which is checked against a simple tree-level process.However, if the tree-level form of the soft theorems is used at sub-sub-leading order even when the elastic amplitude needs resummation, an unphysical IR singularity occurs due to the infinite Coulomb phase. We briefly discuss a recent proposal as how to deal with these divergences and find agreement with the eikonal approach.

We derive the one-instanton effective action of N=4 super Yang-Mills theory in terms of the N=4 on-shell superfields. In the Coulomb branch, instantons correct both the MHV and next-to-next-MHV higher derivative terms D^4F^{2n+2} and F^{2n+4}. We confirm at the non-perturbative level the non-renormalization theorems for MHV F^{2n+2} terms that are expected to receive perturbative corrections only at n-loops. We compute also the one and two-loop corrections to the D^4F^4 term and show that its completion under SL(2,Z) duality is consistent with the one-instanton results.

QMUL Graduate Lectures

QMUL Graduate Lectures

QMUL Graduate Lectures

After reviewing how small BPS black holes with two charges can be described in perturbative Heterotic strings, we compute the cross section for their pair production at tree level and analyze angular and energy distributions. We consider both toroidal compactifications and FHSV orbifold model, and comment on scenari with large extra dimensions. Finally we briefly discuss how to extend our results to non-BPS, non-extremal and rotating BH's.