Research Projects

The fundamental forces in nature—gravity, electromagnetism, the strong, and the weak—are described within different frameworks, with gravity traditionally modeled by Einstein’s general relativity and the others by the Standard Model via gauge theories. Integrating gravity with quantum mechanics remains a central challenge. Black holes are key in this pursuit: they are astrophysical objects identified through direct and indirect observations, yet understanding their quantum interactions with particles involves reconciling classical gravity with quantum field theory (QFT). At high energies, when two scalar particles scatter, the formation of black holes as intermediate states becomes plausible if the energy density is sufficiently concentrated. Unlike standard resonance states with well-defined decay channels, black holes exhibit an exponentially large number of decay modes, leading to an exponential suppression in the probability of specific final states—such as the initial two-particle state. Formulating this scenario involves constructing scattering equations that incorporate these features, posing a challenging problem due to the nonperturbative nature of black hole physics at quantum scales. String theory offers valuable insights: black holes can be characterized thermodynamically via their horizon area, with microstate counting linking entropy to underlying quantum states. When the string coupling is weak, this aligns with semi-classical descriptions, but at strong coupling—where quantum gravity effects are significant—perturbation theory fails, requiring nonperturbative approaches. Developing a model that remains agnostic to the underlying framework but captures these effects is essential. One promising approach involves the S-matrix and dispersion relations. The S-matrix encapsulates all scattering data and is constrained by fundamental principles—unitarity, crossing symmetry, and locality. These constraints relate low-energy data to high-energy (UV) physics, with dispersion relations connecting scattering amplitudes across different energy regimes. The traditional dispersion relation, however, faces convergence issues and inadequately encodes crossing symmetry, complicating the extraction of physical insights. Crossing Symmetric Dispersion Relations (CSDRs) address these limitations by employing building blocks that encode all analytic, kinematic, and asymptotic properties of the amplitude. CSDRs are consistent with string field theory and connect to conformal field theories (CFTs). Given the robust development of the conformal bootstrap—analyzing correlators to constrain operator dimensions—these tools can be adapted to scattering amplitudes, providing a nonperturbative, analytic framework for studying black hole formation. Further, black holes are thermodynamic entities, obeying laws analogous to thermodynamics, and their microscopic origin relates to quantum thermalization and entanglement. Thermalization in this context can be associated with entropic suppression patterns of matrix elements and the emergence of volume-law entanglement. Gravitational scattering that produces black holes can thus be examined to understand under what conditions microscopic chaos leads to thermodynamic behavior. This involves connecting quantum chaos, characterized by exponential out-of-time-ordered correlators, to the statistical emergence of thermodynamics, suggesting a deep link between microscopic dynamics and macroscopic laws. By integrating these insights—nonperturbative dispersion relations, holographic principles, microstate counting, and quantum chaos—we aim to develop a unified, general formalism to describe black hole interactions within quantum scattering processes. This approach seeks to provide a clearer understanding of black hole formation, decay, and their signatures in high-energy experiments, contributing to resolving how gravity behaves at quantum scales and unifying it with the other fundamental interactions.