Physics Research Conference
The von Neumann entropy of a region of space is a notoriously ill-behaved quantity in quantum field theory: it is infinitely big due to short-distance correlations present in the vacuum. In quantum gravity these short-distance correlations can be tamed, leading to the so-called "generalized entropy" of a region of space. For many years, one slogan of quantum gravity has been "Area = Entropy," and I will explain how the concept of generalized entropy allows us to implement this slogan in useful and precise ways. Along the way, we will learn new and interesting things about quantum field theory as seen through the lens of the von Neumann entropy and its more sophisticated cousin, the relative entropy.