Analytic conformal bootstrap at large spin

Thesis

The conformal bootstrap is a powerful method to study conformal field theories, relying only on the existence and associativity of the OPE algebra, and has been used to provide both numeric and analytic constraints on a wide variety of theories. This thesis reviews the ideas of the lightcone bootstrap and large spin perturbation theory, and applies them to constrain the spectrum and algebra of several weakly coupled conformal field theories.

The first part studies the Gross-Neveu and Gross-Neveu-Yukawa models, whose spectrum and algebra are analyzed perturbatively in d = 2 + ε and d = 4 − ε dimensions, respectively. This is achieved by combining the method of twist conformal blocks with constraints from crossing symmetry of correlators of composite operators. Known results for the anomalous dimensions of nearly conserved currents are reproduced, and new results are found for the OPE coefficients and anomalous dimensions of a larger class of operators.

The second part studies the critical O(N) model in two different perturbative regimes, the d = 4 − ε expansion and the large N expansion. In both cases, crossing symmetry of a correlator of fundamental fields is combined with the Lorentzian inversion formula to find anomalous dimensions and OPE coefficients for weakly broken currents to a higher order than previously computed in the literature. In particular these are used to predict central charges in the 3d Ising model, comparing favourably with numerical results and previous predictions.

Authors: van Loon, M

• DOI: 10.5287/ora-eymoxgjqm
• Type of award: DPhil
• Level of award: Doctoral
• Awarding institution: University of Oxford