Entanglement properties of gauge theories and the graviton.

Abstract

Entanglement entropy is emerging as a useful quantity to study critical phenomena in quantum systems, black holes physics, and holography. In this presentation, we discuss entanglement properties of gauge theories and the graviton in the ground state as well as excited states corresponding to local quenches.

We show that the quantum entanglement entropy of the ground state of the free Maxwell field in d=4 dimensions, conformal p-forms, and conformal higher spins can be obtained from the partition function on the hyperbolic cylinder. We demonstrate that the entanglement entropy of linearized gravitons across a sphere coincides with that obtained from the partition function of Kaluza-Klein tower of traceless transverse massive spin-2 fields on the hyperbolic cylinder with the mass of the constant mode along S^1 direction saturating the Brietenholer-Freedman bound in AdS_3.

We show that the Gauss law of gravity implies that certain radial components of Riemann tensors label the super-selection sectors for the graviton. The classical or non-extractable part of the entanglement entropy is evaluated from the two-point functions of certain components of the Riemann tensors on S^2 which coincides with the logarithmic divergent piece of the `edge' partition function of the massless spin-2 field on the 4-sphere when written in terms of its Harish-Chandra character.

We develop a systematic procedure to evaluate the growth in entanglement entropies under local quenches created by free fields with spin, s ≤ 2. We show that in the zero-width limit of the quench, entanglement grows in time and then saturates at log(2) for free fields. The growth profile is determined by order 2s + 1 polynomials in the ratio of the distance from the co-dimension-2 entangling surface and time. The polynomials corresponding to quenches created by the fields can be organized in terms of their representations under the SO(2)_T X SO(2)_L symmetry preserved by the presence of the co-dimension-2 entangling surface.