Abstract
We revisit from a modern bootstrap perspective the longstanding problem of solving Quantum Chromodynamics (QCD) in the large N limit. In particular, we set up a program to carve out the space of large N confining gauge theories using S-matrix bootstrap techniques, with the ultimate goal of cornering large N QCD. We begin by restricting to pion scattering. By simply imposing the full set of positivity constraints that follow from 2 → 2 pion scattering, we already derive universal bounds on the effective field theory (EFT) governing their low-energy interactions. We critically examine our exclusion plots, which exhibit some intriguing connections with hadronic phenomenology, developing in the process an analytic understanding of the geometry of the bounds. Next, we graduate to the case of pions coupled to background electromagnetic fields. We derive the full set of positivity constraints encoded in the system of 2 → 2 scattering amplitudes of pions and photons, and we explore the corresponding bounds. Apart from probing a larger set of intermediate meson states, this system has access to the coefficient of the chiral anomaly. By matching this coefficient with the microscopic theory, we derive bounds that contain an explicit N dependence. Finally, we return to pion scattering, and we make the natural spectral assumption that the 2 → 2 pion amplitude must contain a spin-one rho meson exchange and a massive resonance of spin two. By maximizing the coupling of the latter, we find a very interesting extremal solution of the dual bootstrap problem, which appears to contain at least a full Regge trajectory. Its low-lying states are in uncanny quantitative agreement with the meson masses in the real world.
Year
2024
Document Type
Thesis
Keywords
Bootstrap, Large N, QCD
Degree Name
Doctor of Philosophy (PhD)
Department
Physics
Advisor
Leonardo Rastelli
Recommended Citation
Iglesias, Jan Albert, "Bootstrapping Large N QCD" (2024). Electronic Dissertations and Theses, 2010-current. 137.
https://commons.library.stonybrook.edu/electronic-disserations-theses/137