Energy Flux Positivity and Unitarity in CFTs

TL;DR

This paper demonstrates that in most conformal field theories, the energy flux positivity condition is equivalent to the absence of ghosts, linking unitarity constraints to physical stability at finite temperature.

Contribution

It establishes a precise equivalence between energy flux positivity and ghost absence in CFTs, connecting unitarity conditions to thermal two-point functions of the stress tensor.

Findings

Energy flux positivity implies no ghosts in CFTs.

Two-point functions develop lightlike poles at finite temperature.

Residues of poles relate to energy flux positivity.

Abstract

We show that in most conformal field theories the condition of the energy flux positivity, proposed by Hofman and Maldacena, is equivalent to the absence of ghosts. At finite temperature and large energy and momenta, the two-point functions of the stress energy tensor develop lightlike poles. The residues of the poles can be computed, as long as the only spin two conserved current, which appears in the stress energy tensor OPE and acquires nonvanishing expectation value at finite temperature, is the stress energy tensor. The condition for the residues to stay positive and the theory to remain ghost free is equivalent to the condition of positivity of energy flux.