Constraints on Flavored 2d CFT Partition Functions
This event is part of the Preliminary Oral Exam.
Examining Committee: Liam Fitzpatrick, Ami Katz, Robert Carey, Christopher Laumann
Conformal Field Theory (CFT) relates to many open questions in high-energy physics and condensed matter theory, and brings us important insights into Quantum Gravity via the AdS/CFT correspondence. The conformal bootstrap is a powerful approach to CFT that allows one to study such theories beyond the weakly coupled regime, using only basic universal principles. In this project, we perform a bootstrap analysis on all 2 dimensional CFTs with a conserved charge, using the transformation law for the modular transformation of the CFT’s partition function in the presence of a chemical potential, i.e. flavored partition function. First, we use this law to put constraints on the CFT’s "mass-to-charge" ratio, as well as the weight of charged states in the theory. Then, we apply the extremal functional method to extract the partition functions of the CFTs that saturate the bounds. In several cases we find the prediction of the occupation numbers are precisely integers, which is necessary for a physical theory. Our bounds provide a solid proof of the 3-dimensional Quantum Gravity case of the Weak Gravity Conjecture, and we find some previously inaccessible partition functions.