Thesis

Bootstrapping Conformal Field Theories

• Call:

  FCT / IDPASC call 2012

• Academic Year:

  2012 /2013

• Domain:

  Theoretical Particle Physics

• Supervisor:

  Miguel Costa

• Co-Supervisor:

  João Penedones

• Institution:

  MAP-Fis

• Host Institution:

  Centro de Física do Porto

• Abstract:

  The proposed research program will explore new applications and variations of the numerical bootstrap approach initiated by Rattazzi et al. in 2008. In this seminal work, the authors obtained universal bounds on the conformal dimensions of scalar operators valid in any four dimensional conformal field theory (CFT). More recently, there has been remarkable progress applying the same method to bound the critical exponents of the Ising model in three dimensions. This new approach to CFTs has many applications including beyond the Standard Model physics, phase transitions in statistical physics, quantum critical points in Condensed Matter and quantum gravity through the AdS/CFT duality. Another interesting possibility, is to prove the conjecture that gravity must be the weakest force after using AdS/CFT to translate this statement into CFT language. We plan to generalize the numerical bootstrap approach to other CFTs and to four-point functions of operators with spin. The case of conserved currents can provide universal bounds for CFTs with a given global symmetry. The case of the stress-energy tensor will give rise to completely general bounds for any CFT. We also intend to study variations of the numerical bootstrap method with the goal of finding (approximations to) new CFTs instead of just bounds on the spectrum of dimensions and OPE coefficients. One natural idea is to formulate the problem as a minimization problem in the space of CFT data (dimensions and OPE coefficients). The proposed work will be fully integrated within the international scientific community in the research area of the gauge/gravity duality, particularly through the participation in the ESF research network HoloGrav ; the Marie Curie IRSES network UNIFY, and the recently approved Marie Curie ITN network GATIS.