In quantum gravity, it has been argued that a proper accounting of the role played by an observer promotes the von Neumann algebra of observables in a given spacetime subregion from Type III to Type II. While this allows for a mathematically precise definition of its entropy, we show that this procedure depends on which observer is employed. We make this precise by considering a setup in which many possible observers are present; by generalising previous approaches, we derive density operators for the subregion relative to different observers (and relative to arbitrary collections of observers and for arbitrary global physical states), and we compute the associated entropies in a semiclassical regime, as well as in some specific examples that go beyond this regime. We find that the entropies seen by distinct observers can drastically differ. Our work makes extensive use of the formalism of quantum reference frames (QRF); indeed, as we point out, the ‘observers’ considered here and in the previous works are nothing but QRFs. In the process, we demonstrate that the description of physical states and observables invoked by Chandrasekaran et al. [1] is equivalent to the Page-Wootters formalism, leading to the informal slogan “PW = CLPW”. It is our hope that this paper will help motivate a long overdue union between the QRF and quantum gravity communities. Further details will appear in a companion paper.

A correction to this paper has been published: https://doi.org/10.1007/JHEP07(2025)063

We develop a framework based on the covariant phase space formalism that identifies gravitational edge modes as dynamical reference frames. As such, they enable both the identification of the associated spacetime region and the imposition of boundary conditions in a gauge-invariant manner. While recent proposals considered the finite region in isolation and sought the maximal corner symmetry algebra compatible with that perspective, we here advocate to regard it as a subregion embedded in a global spacetime and study the symmetries consistent with such an embedding. This leads to advantages and differences. It clarifies that the frame, although appearing as "new" for the subregion, is built out of the field content of the complement. Given a global variational principle, it also permits us to invoke a systematic post-selection procedure, previously used in gauge theory [J. High Energy Phys. 02, 172 (2022)], to produce a consistent dynamics for a subregion with timelike boundary. As in gauge theory, requiring the subregion presymplectic structure to be conserved by the dynamics leads to an essentially unique prescription and unambiguous Hamiltonian charges. Unlike other proposals, this has the advantage that all (field-independent) spacetime diffeomorphisms acting on the subregion remain gauge and integrable (as in the global theory), and generate a first-class constraint algebra realizing the Lie algebra of spacetime vector fields. By contrast, diffeomorphisms acting on the frame-dressed spacetime, that we call relational spacetime, are in general physical, and those that are parallel to the timelike boundary are integrable. Upon further restriction to relational diffeomorphisms that preserve the boundary conditions (and hence are symmetries), we obtain a subalgebra of conserved corner charges. Physically, they correspond to reorientations of the frame and so to changes in the relation between the subregion and its complement. Finally, we explain how the boundary conditions and conserved presymplectic structure can both be encoded into boundary actions. While our formalism applies to any generally covariant theory, we illustrate it on general relativity, and conclude with a detailed comparison of our findings to earlier works.

The Eigenstate Thermalization Hypothesis (ETH) has played a key role in recent advances in the high energy and condensed matter communities. It explains how an isolated quantum system in a far-from-equilibrium initial state can evolve to a state that is indistinguishable from thermal equilibrium, with observables relaxing to almost time-independent results that can be described using traditional statistical mechanics ensembles. In this work we probe the limits of ETH, pushing it outside its prototypical applications in several directions. We design a qutrit lattice system with conserved quasilocal charge, in which we verify a form of generalized eigenstate thermalization. We also observe signatures of thermalization in states well outside microcanonical windows of both charge and energy, which we dub `generic ETH.'

We explore the effect of introducing mild nonlocality into otherwise local, chaotic quantum systems, on the rate of information spreading and associated rates of entanglement generation and operator growth. We consider various forms of nonlocality, both in 1-dimensional spin chain models and in holographic gauge theories, comparing the phenomenology of each. Generically, increasing the level of nonlocality increases the rate of information spreading, but in lattice models we find instances where these rates are slightly suppressed.

We present a general theory of quantum information propagation in chaotic quantum many-body systems. The generic expectation in such systems is that quantum information does not propagate in localized form; instead, it tends to spread out and scramble into a form that is inaccessible to local measurements. To characterize this spreading, we define an information speed via a quench-type experiment and derive a general formula for it as a function of the entanglement density of the initial state. As the entanglement density varies from zero to one, the information speed varies from the entanglement speed to the butterfly speed. We verify that the formula holds both for a quantum chaotic spin chain and in field theories with an AdS/CFT gravity dual. For the second case, we study in detail the dynamics of entanglement in two-sided Vaidya-AdS-Reissner-Nordstrom black branes. We also show that, with an appropriate decoding process, quantum information can be construed as moving at the information speed, and, in the case of AdS/CFT, we show that a locally detectable signal propagates at the information speed in a spatially local variant of the traversable wormhole setup.

We study holographic subregion complexity, and its possible connection to purification complexity suggested recently by Agon et al. In particular, we study the conjecture that subregion complexity is the purification complexity by considering holographic purifications of a holographic mixed state. We argue that these include states with any amount of coarse-graining consistent with being a purification of the mixed state in question, corresponding holographically to different choices of the cutoff surface. We find that within the complexity = volume and complexity = spacetime volume conjectures, the subregion complexity is equal to the holographic purification complexity. For complexity = action, the subregion complexity seems to provide an upper bound on the holographic purification complexity, though we show cases where this bound is not saturated. One such example is provided by black holes with a large genus behind the horizon, which were studied by Fu et al. As such, one must conclude that these offending geometries are not holographic, that CA must be modified, or else that holographic subregion complexity in CA is not dual to the purification complexity of the corresponding reduced state.

We study the holographic complexity of noncommutative field theories. The four-dimensional \( \mathcal{N}=4 \) noncommutative super Yang-Mills theory with Moyal algebra along two of the spatial directions has a well known holographic dual as a type IIB supergravity theory with a stack of D3 branes and non-trivial NS-NS B fields. We start from this example and find that the late time holographic complexity growth rate, based on the “complexity equals action” conjecture, experiences an enhancement when the non-commutativity is turned on. This enhancement saturates a new limit which is exactly 1/4 larger than the commutative value. We then attempt to give a quantum mechanics explanation of the enhancement. Finite time behavior of the complexity growth rate is also studied. Inspired by the non-trivial result, we move on to more general setup in string theory where we have a stack of Dp branes and also turn on the B field. Multiple noncommutative directions are considered in higher p cases.

The previously proposed “Complexity=Volume” or CV-duality is probed and developed in several directions. We show that the apparent lack of universality for large and small black holes is removed if the volume is measured in units of the maximal time from the horizon to the “final slice” (times Planck area). This also works for spinning black holes. We make use of the conserved “volume current”, associated with a foliation of spacetime by maximal volume slices, whose flux measures their volume. This flux picture suggests that there is a transfer of the complexity from the UV to the IR in holographic CFTs, which is reminiscent of thermalization behavior deduced using holography. It also naturally gives a second law for the complexity when applied at a black hole horizon. We further establish a result supporting the conjecture that a boundary foliation determines a bulk maximal foliation without gaps, establish a global inequality on maximal volumes that can be used to deduce the monotonicity of the complexification rate on a boost-invariant background, and probe CV duality in the settings of multiple quenches, spinning black holes, and Rindler-AdS.

It has recently been shown that the presence of a spectator pseudoscalar field, coupled to photons through a Chern-Simons term, can amplify the primordial tensor spectrum without observationally disrupting the primordial scalar spectrum. The amplification occurs due to an instability that develops for the vector fields. We consider the extension of previous studies to account for the contribution arising from an inhomogeneous vector background which is generated prior to the onset of inflation. We find that there may be contributions in which net momentum is transferred between the inhomogeneous vector background and the gravitons, which would give rise to a signature different than in the absence of the semiclassical corrections. We discuss the properties the classical vector field form must have in order for these signatures to leave observable imprints, though we were unable to construct a model for generating such a vector field.