Entanglement entropy of gravitational edge modes

Abstract

We consider the linearised graviton in 4d Minkowski space and decompose it into tensor spherical harmonics and fix the gauge. The Gauss law of gravity implies that certain radial components of the Riemann tensor of the graviton on the sphere labels the superselection sectors for the graviton. We show that among these 6 normal components of the Riemann tensor, 2 are related locally to the algebra of gauge-invariant operators in the sphere. From the two-point function of these components of the Riemann tensor on S2 we compute the logarithmic coefficient of the entanglement entropy of these superselection sectors across a spherical entangling surface. For sectors labelled by each of the two components of the Riemann tensor these coefficients are equal and their total contribution is given by $$ -\frac{16}{3} $$ − 16 3 . We observe that this coefficient coincides with that extracted from the edge partition function of the massless spin-2 field on the 4-sphere when written in terms of its Harish-Chandra character. As a preliminary step, we also evaluate the logarithmic coefficient of the entanglement entropy from the superselection sectors labelled by the radial component of the electric field of the U(1) theory in even d dimensions. We show that this agrees with the corresponding coefficient of the edge Harish-Chandra character of the massless spin-1 field on Sd.

Entanglement entropy of local gravitational quenches

“…Therefore the 'split property' of quantum local field theories does not hold in the theory of quantum gravity. From this paper as well as the earlier work [27][28][29], we see that the theory of linearised gravitons behaves just as a local quantum field theory JHEP04(2023)028 with gauge symmetry. It will be interesting to see explicitly how this behavior departs from that of a local quantum field theory once the theory becomes interacting.…”

“…The coefficient of the logarithmic term for the entanglement entropy of a spherical region in a theory of linearized gravitons has been evaluated in [27,28]. The contribution to the entropy from gravitational edge modes has been understood in [29]. The graviton after all is a fundamental particle of nature, and therefore it is useful and important to study its information theoretic properties.…”

Pseudo Entropy in U(1) gauge theory

“…But, one can also evaluate the difference between pseudo entanglement entropy and ground state entanglement entropy in the particular region of the parameter space α = 1 2 (α 2 − α 1 ), where α 1 = −it − and α 2 = −it + are the two Euclidean times where the field strengths are placed. Note that, in the limit α = → 0, JHEP10(2022)016 the correlators on the same sheet and the correlators across the sheets have the leading contribution in ∆S (n) A as shown in [19][20][21][22] for conformal scalar and free Maxwell field and recently in [24] for the local gravitational excitations. Therefore, in the limit α → 0, one can extract the leading term in the expression of ∆S A .…”

Entanglement and geometry from subalgebras of the Virasoro

“…In fact, this type of Hamiltonian has appeared in the study of quantum quenches, such as the Möbius quench and the SSD quench. 21 The techniques and the dual bulk geometries in our work can serve as building blocks for the holographic understanding of the quench dynamics in those deformed models or related questions with excited states. Some progress in this direction has been already reported in [84][85][86][87][88] and more will be presented in the future work [89].…”

“…Their holographic dual involves a dynamical geometry that can be obtained from the back-reaction of a massive particle (or generally a bulk field), which is dual to that local operator [19]. In particular, entanglement evolution in these states has been studied extensively in the context of quantum quenches [20][21][22][23][24][25][26][27], scrambling [28,29], quantum chaos [30][31][32][33] as well as bulk reconstruction in AdS/CFT [34][35][36]. Certainly, this family provides very important and analytically tractable data points in the "spacetime from entanglement" program.…”