Thesis

Exploring conformal bootstrap at higher points

• Call:

  PT-CERN Call 2022/2

• Academic Year:

  2022

• Domain:

  Astroparticle Physics

• Supervisor:

  Miguel Costa

• Co-Supervisor:

  Vasco David Fonseca Gonçalves

• Institution:

  Universidade do Porto

• Host Institution:

  CF-UM-UP - Centro de Física das Universidades do Minho e do Porto

• Abstract:

  Quantum field theory(QFT) is quintessential to describe diverse physical phenomena spanning from condensed matter systems to particle collisions in high energy accelerators. Even more, it is one of our best hopes to unify quantum theory with gravity, with the Anti de Sitter/conformal field theory (AdS/CFT) duality being one of the prime examples where this is possible. However an important part of physical systems have a strongly coupled nature and thus evade most of the theoretical methods to tackle these problems. For instance, there is no good theoretical method to describe confinement or the existence of a mass gap. Advances in these questions, even if in toy models, would have a significant impact in theoretical physics. Fortunately, there has been progress during the last decades to develop and explore new non-perturbative approaches to describe quantum field theories at finite coupling. One of them is based on the old idea of deriving constraints from imposing consistency conditions based on the symmetries of the underlying theories. This is the essence of the by now famed conformal and S-matrix bootstrap programs. An important problem that only recently has become more tractable to bootstrap methods is the understanding of the structure of higher point functions in conformal field theories. The aim of this project is to explore the consistency conditions imposed by symmetry on these more complex objects. This is an ambitious program with implications for quantum gravity, CFTs and also QFT’s in general.