How negative can null energy be in large N CFTs?

TL;DR

This paper investigates the lower bounds of smeared null energy in large N conformal field theories, suggesting it is limited by the central charge, which has implications for energy conditions in quantum field theories.

Contribution

It provides the first analysis of negative null energy bounds in interacting large N CFTs in dimensions greater than two, proposing a bound proportional to the central charge.

Findings

Negative null energy scales at worst with the central charge $C_T$

States constructed from scalar primaries or stress-energy tensor can have unbounded energy in free theories

Evidence for a universal bound on null energy in large N CFTs

Abstract

Smeared null energy has been shown to be bounded from below for free minimally coupled quantum field theories. This is not the case for conformally coupled free bosonic theories where states of unbounded null energy can be constructed by increasing the particle number. Little is known for interacting conformal field theories (CFTs) in dimensions larger than two. In this work we consider states that are superpositions of scalar primary operators or the stress-energy tensor itself in large N CFTs. Within the large N approximation we present arguments that the negative smeared null energy of such states scales at worst as the central charge of theory, $C_T$. This provides evidence for a general bound for CFTs in d-dimensions proportional to the central charge.