Christopher J. Fewster, Stefan Hollands
Quantum Energy Inequalities in Two-Dimensional Conformal Field Theory
Preprint series: ESI preprints

MSC:

81T40 Two-dimensional field theories, conformal field theories, etc.

PACS: 11.25.Hf,3.70.+k
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 theori
es.
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.

Keywords: Quantum inequalities, conformal field theory