Part III Essay: Varieties of Locality for Quantum Fields and Strings (Essay Number 57)

In recent years, a new paradigm in theoretical physics has emerged known as the holographic principle. This principle states that the number of degrees of freedom in a d-dimensional region of a (d + 1)-dimensional spacetime is proportional to the area of a suitably defined surface associated with the region of spacetime. This principle was motivated by the fact that the entropy of a black hole is in fact proportional to the area, rather than the volume, of the event horizon. Over the years, this entropy bound on black holes has been extended to more general settings, culminating in the formulation of the covariant entropy bound. Nonetheless, there is still much controversy surrounding the holographic principle, as it violates locality and also contradicts the principles of traditional quantum field theories. This paper will both motivate the development of the holographic principle, beginning with the entropy of black holes and ending with the covariant entropy bound for arbitrary spacetime geometries, as well as explore the tensions between locality and the holographic principle.