Quantum Energy Inequalities in two-dimensional conformal field theory

TL;DR

This paper establishes rigorous quantum energy inequality bounds for a broad class of interacting two-dimensional conformal field theories, including minimal and rational models, independent of quantum states.

Contribution

It provides the first state-independent QEI bounds for interacting 2D conformal field theories, extending previous free-field results to a wider class of models.

Findings

QEI bounds depend on averaging weight and central charge, not on quantum state.

Results apply to timelike, null, spacelike curves, and spacetime volumes.

Includes boundary CFTs and moving mirror models.

Abstract

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 spacetime volume. In addition, we consider boundary conformal field theories and more general 'moving mirror' models. Our results hold for all theories obeying a minimal set of axioms which -- as we show -- are satisfied by all models built from unitary highest-weight representations of the Virasoro algebra. In particular, this includes all (unitary, positive energy) minimal models and rational conformal field theories. Our discussion of this issue collects together (and, in places, corrects) various results from the literature which do not appear to have been assembled in this form elsewhere.