  We study the vacuum-subtracted von Neumann entropy of a segment on a null
plane. We argue that for interacting quantum field theories in more than two
dimensions, this entropy has a simple expression in terms of the expectation
value of the null components of the stress tensor on the null interval. More
explicitly $\Delta S = 2\pi \int d^{d-2}y \int_0^1 dx^+\, g(x^+)\, \langle
T_{++}\rangle$, where $g(x^+)$ is a theory-dependent function. This function is
constrained by general properties of quantum relative entropy. These
constraints are enough to extend our recent free field proof of the quantum
Bousso bound to the interacting case.
  This unusual expression for the entropy as the expectation value of an
operator implies that the entropy is equal to the modular Hamiltonian, $\Delta
S = \langle \Delta K \rangle $, where $K$ is the operator in the right hand
side. We explain how this equality is compatible with a non-zero value for
$\Delta S$. Finally, we also compute explicitly the function $g(x^+)$ for
theories that have a gravity dual.

High Energy Physics - Theory