Cardy's Conjecture and the Spectrum of Infrared Strongly-Coupled Quantum Field Theories
Abstract
Cardy's conjecture about the evolution of the trace anomaly under renormalization group (RG) flows is re-interpreted as an exact, non-perturbative statement about the scaling dimension of terms in the Lagrangian of the theory. When viewed in this way, the conjecture implies that field theories which are strongly coupled in the infrared (IR) may generically host states that are not manifest as solutions to the ultraviolet (UV) complete theory's equations of motion. In particular, the scaling dimension of operators in the Hamiltonian may deviate from their classical values by O(1) corrections in the IR, circumventing an old argument by Derrick about the non-existence of such states1. We show that this framework provides a natural way to estimate the masses of these states using perturbation theory, and suggests a preferred reorganization of the degrees of freedom in the IR.