Bootstrap methods for collider physics.
1. Nonperturbative scattering amplitudes.
We have initiated a research program and developed tools to construct relativistic nonperturbative scattering amplitudes that obey analyticity, unitarity, and crossing. The S-matrix bootstrap exploits a subtle tension between causality and quantum-mechanical unitarity. In a conventional perturbative approach, these properties are implemented using Feynman diagrams. This, however, leads to a divergent perturbative expansion. In contrast, we have developed a nonperturbative algorithm that retains many desirable features of the Feynman expansion while leading to a convergent expansion of the amplitude. Under simplifying assumptions, we have solved this problem for scalar scattering in two, three, and four spacetime dimensions. The key recent development was the adoption of machine learning techniques, parameterizing the amplitude by a neural network. We plan to continue pushing this program toward more realistic amplitudes, such as those expected in QCD and make our software public.
2. Gravitational and stringy amplitudes.
We have established a few basic facts about gravitational scattering. For massive particles in QFT, it has been known since the 1960s that the possible growth of the amplitude with energy is bounded by the fourth power of the scattering energy. Using the known properties of gravity at large distances, we have established the same bound for scattering in gravity. The significance of this bound lies in the ability to write dispersion relations, which allow one to explore the consequences of UV consistency for IR observations. We have analyzed a finite-coupling deformation of the Veneziano amplitude using integrability, the S-matrix bootstrap, and perturbative methods. It exhibits curved Regge trajectories reminiscent of those in QCD, as well as rich physics interpolating between familiar Feynman diagrams at weak coupling and the Veneziano amplitude at strong coupling.
3. Event shapes and light-ray operators. Energy correlations between produced particles are directly measured at the LHC. In recent years, a new connection has emerged between these standard collider observables and the theory of light-ray operators. It led to the development of a new nonperturbative expansion, called the light-ray OPE, which controls the behavior of energy correlations when the angular separation between detectors becomes small. This is instructive for understanding jet substructure in QCD. In the course of the project, we have extended our understanding of energy correlations by introducing a nontrivial working-time profile for detectors, and by studying general properties of energy correlations in multi-particle, or heavy, states. Recently, we also applied bootstrap methods to these observables, obtaining them at finite coupling in N=4 SYM, both in the planar limit and at finite Nc. This became possible by combining conformal-bootstrap dispersive functionals with supersymmetric localization.
Bootstrap methods for holography and black holes.
1. Consistency conditions for gravitational EFTs. It is believed that, given a strongly coupled CFT with many degrees of freedom, a large gap, and a large central charge, its dual description is given by classical gravity. Establishing this conjecture remains an open problem. One part of this conjecture, recently proven rather rigorously and explored in this project, puts bounds on the Wilson coefficients that enter four-graviton scattering in terms of the masses of higher-spin particles. More precisely, we have analyzed such bounds using dispersion relations for graviton scattering in four dimensions. We have also analyzed the graviton pole and its emergence from a microscopic theory using dispersion relations, which allowed us to sharpen the definition of the species scale, an important notion in the modern swampland program.
2. Black holes, finite temperature, large charge. In holography, black-hole physics is mapped to finite-temperature physics of the dual theory. Understanding how spacetime emerges in quantum gravity thus requires understanding thermal properties of strongly coupled QFTs. We have initiated a systematic study of the thermal two-point function in holographic theories and derived several important and novel results. We have worked out the connection between gravitational orbits around black holes, double-twist operators in the conformal bootstrap, and quantum many-body scars discussed in the condensed matter literature. We also used state-of-the-art results in mathematical physics to find the exact thermal two-point function in terms of Nekrasov functions and to provide the all-order solution to the light-cone bootstrap. We have put forward a product formula expressing the thermal two-point function in terms of quasi-normal modes and studied its general properties as dictated by the short-distance behavior of the correlator. We have pointed out that a smoking gun of an emergent black-hole geometry is a pattern of bulk-cone singularities, which we have characterized. Finally, we have studied a two-point function of light-ray operators in heavy, large-charge states and proposed a general formula for energy correlations in such states.
