Symmetries and charges of general relativity at null boundaries

We study general relativity at a null boundary using the covariant phase space formalism. We define a covariant phase space and compute the algebra of symmetries at the null boundary by considering the boundary-preserving diffeomorphisms that preserve this phase space. This algebra is the semi-direct sum of diffeomorphisms on the two sphere and a nonabelian algebra of supertranslations that has some similarities to supertranslations at null infinity. By using the general prescription developed by Wald and Zoupas, we derive the localized charges of this algebra at cross sections of the null surface as well as the associated fluxes. Our analysis is covariant and applies to general non-stationary null surfaces. We also derive the global charges that generate the symmetries for event horizons, and show that these obey the same algebra as the linearized diffeomorphisms, without any central extension. Our results show that supertranslations play an important role not just at null infinity but at all null boundaries, including non-stationary event horizons. They should facilitate further investigations of whether horizon symmetries and conservation laws in black hole spacetimes play a role in the information loss problem, as suggested by Hawking, Perry, and Strominger.Comment: v2: added appendices on trivial diffeomorphisms and relation to 1810.01847; v1: 59 pages + appendices, 2 figure

Large N algebras and generalized entropy

We construct a Type II$_\infty$ von Neumann algebra that describes the large $N$ physics of single-trace operators in AdS/CFT in the microcanonical ensemble, where there is no need to include perturbative $1/N$ corrections. Using only the extrapolate dictionary, we show that the entropy of semiclassical states on this algebra is holographically dual to the generalized entropy of the black hole bifurcation surface. From a boundary perspective, this constitutes a derivation of a special case of the QES prescription without any use of Euclidean gravity or replicas; from a purely bulk perspective, it is a derivation of the quantum-corrected Bekenstein-Hawking formula as the entropy of an explicit algebra in the $G \to 0$ limit of Lorentzian effective field theory quantum gravity. In a limit where a black hole is first allowed to equilibrate and then is later potentially re-excited, we show that the generalized second law is a direct consequence of the monotonicity of the entropy of algebras under trace-preserving inclusions. Finally, by considering excitations that are separated by more than a scrambling time we construct a "free product" von Neumann algebra that describes the semiclassical physics of long wormholes supported by shocks. We compute R\'{e}nyi entropies for this algebra and show that they are equal to a sum over saddles associated to quantum extremal surfaces in the wormhole. Surprisingly, however, the saddles associated to "bulge" quantum extremal surfaces contribute with a negative sign.Comment: 57 pages + appendice

Asymptotic Charges Cannot Be Measured in Finite Time

To study quantum gravity in asymptotically flat spacetimes, one would like to understand the algebra of observables at null infinity. Here we show that the Bondi mass cannot be observed in finite retarded time, and so is not contained in the algebra on any finite portion of ${\mathscr{I}}^+$. This follows immediately from recently discovered asymptotic entropy bounds. We verify this explicitly, and we find that attempts to measure a conserved charge at arbitrarily large radius in fixed retarded time are thwarted by quantum fluctuations. We comment on the implications of our results to flat space holography and the BMS charges at ${\mathscr{I}}^+$.Comment: 9 pages, 3 figures. v2 typos fixed and minor addition

Higher-Point Positivity

We consider the extension of techniques for bounding higher-dimension operators in quantum effective field theories to higher-point operators. Working in the context of theories polynomial in $X=(\partial \phi)^2$, we examine how the techniques of bounding such operators based on causality, analyticity of scattering amplitudes, and unitarity of the spectral representation are all modified for operators beyond $(\partial \phi)^4$. Under weak-coupling assumptions that we clarify, we show using all three methods that in theories in which the coefficient $\lambda_n$ of the $X^n$ term for some $n$ is larger than the other terms in units of the cutoff, $\lambda_n$ must be positive (respectively, negative) for $n$ even (odd), in mostly-plus metric signature. Along the way, we present a first-principles derivation of the propagator numerator for all massive higher-spin bosons in arbitrary dimension. We remark on subtleties and challenges of bounding $P(X)$ theories in greater generality. Finally, we examine the connections among energy conditions, causality, stability, and the involution condition on the Legendre transform relating the Lagrangian and Hamiltonian.Comment: 25 page

A Tale of Two Saddles

We find a new on-shell replica wormhole in a computation of the generating functional of JT gravity coupled to matter. We show that this saddle has lower action than the disconnected one, and that it is stable under restriction to real Lorentzian sections, but can be unstable otherwise. The behavior of the classical generating functional thus may be strongly dependent on the signature of allowed perturbations. As part of our analysis, we give an LM-style construction for computing the on-shell action of replicated manifolds even as the number of boundaries approaches zero, including a type of one-step replica symmetry breaking that is necessary to capture the contribution of the new saddle. Our results are robust against quantum corrections; in fact, we find evidence that such corrections may sometimes stabilize this new saddle.Comment: 48 + 26 pages, 26 figure