In this thesis, we analyze unitary conformal field theories in three dimensional spaces via analytic techniques of conformal bootstrap program through correlation functions of nonscalar operators, in particular Majorana fermions. Via the analysis of these correlation functions, we access several sectors in the spectrum of conformal field theories that have been previously unexplored with analytic methods, and we provide new data for several operator families. In the first part of the thesis, we achieve this by the large spin expansions that have been traditionally used in conformal bootstrap program for scalar correlators, whereas in the second part we carry out the computations by combining several analytic tools that have been recently developed such as the Lorentzian inversion formula and the weight shifting operators with the harmonic analysis for the Euclidean conformal group. We compare these methods and demonstrate the superiority of the latter by computing correction terms that are inaccessible in the former. A better analytic grasp of the spectrum of fermionic conformal field theories can help in many directions including making new precise analytic predictions for supersymmetric models, computing the binding energies of fermions in curved space, and describing quantum phase transitions in condensed matter systems with emergent Lorentz symmetry.
Thesis Advisor: David Poland (david.poland@yale.edu)
Contact Stacey Watts for zoom information.