Quantum energy inequalities in two-dimensional conformal field theory

Quantum energy inequalities (QEIs) are state-independent lower bounds on weighted averages of the stress-energy tensor, and have been established for several free quantum field models. We present rigorous QEI bounds for a class of interacting quantum fields, namely the unitary, positive energy conformal field theories (with stress-energy tensor) on two-dimensional Minkowski space. The QEI bound depends on the weight used to average the stress-energy tensor and the central charge(s) of the theory, but not on the quantum state. We give bounds for various situations: averaging along timelike, null and spacelike curves, as well as over a space-time volume. In addition, we consider boundary conformal field theories and more general "moving mirror" models.