UC San Diego

We study various aspects of scale invariant quantum field theories, in particular, the non-relativistic ones. We explore consequences of symmetry algebra in terms of unitarity bound, existence of monotonic renormalization group flow. We leverage the non relativistic conformal symmetry algebra to construct an operator basis for Heavy Quark Effective Field theory and thereby provide a framework for operator counting in this effective field theory. We investigate the large charge sector of non-relativistic conformal theory and in that limit, we find the scaling of operator dimensions with respect to the charge it carries. In the relativistic counterpart, we focus on 2D conformal field theories (CFT) and explore the consequences of modular invariance of thermal partition function of a 2D CFT. In particular, we investigate the finer details of the asymptotic density of states in 2D CFT using modular invariance and put bounds on asymptotic gap in the spectra.