Rajeev Erramilli

I present the design, development, and application of new technology for the conformal bootstrap in the context of the study of three-dimensional conformal field theories (CFTs) with fermionic operators, as well as an exploration of the bootstrap of a fermionic gauge CFT. In doing so, we find world-record-precision rigorous bounds on the critical exponents and OPE coefficients of the O(N) Gross-Neveu-Yukawa (GNY) family of CFTs for N=2,4,8 as well as significant progress in the bootstrap of Quantum Electrodynamics in 2+1 dimensions (QED3). First, we derive closed-form expressions for all ingredients of the Zamolodchikov-like recursion relation for general spinning conformal blocks in 3-dimensional CFT. Our derivation is based on an understanding of null states and conformally-invariant differential operators in momentum space, combined with a careful choice of the relevant tensor structures bases. Based on this result, we then design an algorithm for these conformal block computations to compute conformal blocks for correlation functions of operators of general spin without ad-hoc computations, representing an improvement over previous efforts. This algorithm is implemented as a heavily optimized, multithreaded, C++ application, blocks_3d. We then use blocks_3d to perform a bootstrap analysis using supercomputing clusters of a mixed system of four-point functions of bosonic and fermionic operators providing rigorous bounds on the scaling dimensions of the O(N) GNY fixed points and constraining these theories to live in isolated islands in the space of CFT data. We focus on the cases N=1,2,4,8, which have applications to phase transitions in condensed matter systems, and compare our bounds to previous analytical and numerical results. Finally, we perform a bootstrap analysis of critical Nf=4 QED3, a theory of fermions with a U(1) gauge field. Notably, we constrain the scaling dimensions of the leading fermion bilinear and leading monopole operator to a closed island, suggesting that our large-Nf-inspired assumptions can form a self-consistent CFT despite not being strictly justified.