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Spacetime emergence from entanglement has long been presumed to be holographic, with emergence from quantum interactions in a boundary theory. Since that setup is difficult to extend to general spacetimes, it is imperative to understand the key aspects of the map from entanglement to spacetime. We consider a scenario for spacetime emergence from quantum interactions directly in the spacetime, where the effective spacetime theory emerges from interactions similar to how fluid dynamics arises from molecule interactions. We show that this ansatz constitutes a working scenario for spacetime emergence in 2D, with explicit examples for AdS and dS spacetimes. Importantly, by basing the emergence on interactions between quantum fluctuations that are present in the spacetime, key aspects of the dynamics observed in gauge/gravity duality analyses can be retained, at the same time as the quantisation can be applied to general spacetimes., Comment: 21 pages. v2: text added to {\S}1, {\S}4 rewritten for clarification + minor modifications

We describe how a model of effective interactions between quantum fluctuations under certain assumptions can be constructed in a way so that the large-scale limit gives an effective theory that matches general relativity in vacuum regions. This is an investigation of a possible scenario of spacetime emergence from quantum interactions directly in the spacetime, and of how effective quantum behaviour might provide a useful link between detailed properties of quantum interactions and general relativity. The quantum fluctuations are assumed to entangle sufficiently for a cohesive spacetime to form, so that their effective properties can be described relative to a D-dimensional reference frame. To obtain the desired features of a smooth metric with a vanishing Ricci tensor, the quantum fluctuations are modelled as Gaussian probability distributions, with a shape set relative to the interactions coming from the surroundings. At small scales, the propagation through the spacetime is modelled by a Gaussian random walk., Comment: 27 pages, journal reference added

In a close look at the replica wormhole derivation of the island conjecture, we note a discrepancy in the derived matrix eigenvalues in the limit where the Hawking radiation entropy goes to zero. The small corrections to the density matrix for the radiation infer that ${\rm tr}(\rho_\textsf{R}^2)$, equally a sum over the eigenvalues squared, must be small ($\ll1$) at all times. This is in contradiction with an ensemble dominated by a density matrix with an eigenvalue close to unity. Also, the radiation entropy has been approximated by the ensemble averaged entropy, as in a final state analysis. For $\rho_\textsf{R}=\rho_\textsf{R}(\sigma)$ with $\sigma$ the set of variables used in the average, the ensemble average is only an accurate estimate of the entropy after $\sigma$ has been measured. At the formation of each Hawking pair, there is a distribution over $\sigma$ that affects the entropy. Without a real time determination of $\sigma$, the radiation entropy follows Hawking's result during the evaporation. A question remains of how quickly such determinations can be assumed to occur. A complete argument for that the radiation entropy follows the Page curve should address this., Comment: 14 pages. v2: references and a footnote added

We argue that the `island conjecture' and the replica wormhole derivation of the Page curve break monogamy of entanglement through allowing black hole interior states to be non-classically correlated while also pairwise entangled with radiation states. The reason is that quantum degrees of freedom (present in any half of a Hawking pair) cannot all be identified with the environment at semi-classical pair production, and can only be fixed relative to a subsystem, as required for the Page curve, by correlations equivalent to entanglement - regardless of what those correlations are attributed to. This implies that the recent gravity (replica wormhole) and holographic (island conjecture) derivations of the Page curve entail new physics not yet properly taken into account., Comment: 10 pages. v2: references added, text added to \S 3

In density matrix theory, entanglement is monogamous. However, we show that qubits can be arbitrarily entangled in a different, recently constructed model of qubit entanglement [arXiv:1907.11805]. We illustrate the differences between these two models, analyse how the density matrix property of monogamy of entanglement originates in assumptions of classical correlations in the construction of that model, and explain the counterexample to monogamy in the alternative model. We conclude that monogamy of entanglement is a theoretical assumption, not necessarily a physical property, and discuss how contemporary theory relies on that assumption. The properties of entanglement entropy are very different in the two models; a priori, the entropy in the alternative model is classical., Comment: 19 pages. v2: added \S 1.2, \S 4 shortened, appendices edited

We show how the Bell correlations can be modelled locally by relaxing the joint probability relation for independent variables $P(a,b)=P(a)P(b)$ outside classical settings, with complex/quaternion generators for the measurement outcomes encoding a deviation from this (classical) requirement. The consideration is motivated by complementarity. We analyse the pair correlations (photons or spin 1/2 particles) based on the limitations put on complementary observables when they are modelled as classical, non-commuting operators. As complementarity comes with both single particle properties and correlations insufficiently captured by classical theory together with `non-commutativity', we argue that a complete model should allow complementary observables to have new local dependences. That is, the existing information should not be restricted to be classical (simultaneously observable). Given this new correlation model, the central question is if information theory ought to be extended accordingly in quantum physics., Comment: 10 pages. v2: added summary; v3: extended introduction, references added

Electron solid phases of matter are revealed by characteristic vibrational resonances. Sufficiently large magnetic fields can overcome the effects of disorder, leading to a weakly pinned collective mode called the magnetophonon. Consequently, in this regime it is possible to develop a tightly constrained hydrodynamic theory of pinned magnetophonons. The behavior of the magnetophonon resonance across thermal and quantum melting transitions has been experimentally characterized in two-dimensional electron systems. Applying our theory to these transitions we explain several key features of the data: (i) violation of the Fukuyama-Lee sum rule as the transition is approached is directly tied to the non-Lorentzian form taken by the resonance and (ii) the non-Lorentzian shape is caused by characteristic dissipative channels that become especially important close to melting: proliferating dislocations and uncondensed charge carriers., Comment: 20+4 pages. 4 figures

We consider a hypothesis in which classical space-time emerges from information exchange (interactions) between quantum fluctuations in the gravity theory. In this picture, a line element would arise as a statistical average of how frequently particles interact, through an individual rate $dt\sim 1/f_t$ and spatially interconnecting rates $dl\sim c/f$. The question is if space-time can be modelled consistently in this way. The ansatz would be opposite to the standard treatment of space-time as insensitive to altered physics at event horizons (disrupted propagation of information) but by extension relate to the connection of space-time to entanglement (interactions) through the gauge/gravity duality. We make a first, rough analysis of the implications this type of quantization would have on the classical structure of flat space-time, and of what would be required of the interactions. Seeing no obvious reason for why the origin would be unrealistic, we comment on expected effects in the presence of curvature., Comment: 22 pages. v3: extended introduction

A scenario of space-time emergence from individual interactions at the quantum level requires correlations encoding a scalar product, for large-scale emergence of space orientation. In D=4 the candidate is spin 1/2 correlations, indicating complementarity to be crucial in models of correlations, entangling processes and thermalization giving rise to space-time. We argue for the relevance of identifying fundamental interactions and of analysing how they might give rise to space-time emergence. We discuss how to model complementarity locally, contrasting with how it is absent in the wave function due to a restriction to classically simultaneous variables. In modelling theory after measurements, we suggest an extended model to contain `orthogonal' information existing in parallel, in a vector analogy. We also give a rough conjecture of what would be required of entangling processes for equilibration of correlations between vacuum fluctuations, only briefly mentioning effects of acceleration., Comment: 7 pages. v3: minor clarifications added

The characteristics of tree level scattering amplitudes in theories with nonlinear (super)symmetries were recently proposed by Kallosh to be encoded in a simple way directly from the action, based on a background field method. We check this conjecture to lowest non-trivial order in the Volkov-Akulov theory, where the local 6-point diagram cancels and the results up to 6 points indeed are in agreement with S-matrix computations., Comment: 13 pages. v2: refs. added. v3: refs added, intro and discussion improved

We describe the collective hydrodynamic motion of an incommensurate charge density wave state in a clean electronic system. Our description simultaneously incorporates the effects of both pinning due to weak disorder and also phase relaxation due to proliferating dislocations. We show that the interplay between these two phenomena has important consequences for charge and momentum transport. For instance, it can lead to metal-insulator transitions. We furthermore identify signatures of fluctuating density waves in frequency and spatially resolved conductivities. Phase disordering is well known to lead to a large viscosity. We derive a precise formula for the phase relaxation rate in terms of the viscosity in the dislocation cores. We thereby determine the viscosity of the superconducting state of BSCCO from the observed melting dynamics of Abrikosov lattices and show that the result is consistent with dissipation into Bogoliubov quasiparticles., Comment: 1+24+10 pages + refs, 6 figures; v2, extended discussion of phase relaxation; v3, moved detailed discussion of review material to appendices to shorten main text; v4, presentation improved and shortened

Bad metals have a large resistivity without being strongly disordered. In many bad metals the Drude peak moves away from zero frequency as the resistivity becomes large at increasing temperatures. We catalogue the position and width of the `displaced Drude peak' in the observed optical conductivity of several families of bad metals, showing that $\omega_\text{peak} \sim \Delta \omega \sim k_BT/\hbar$. This is the same quantum critical timescale that underpins the $T$-linear dc resistivity of many of these materials. We provide a unified theoretical description of the optical and dc transport properties of bad metals in terms of the hydrodynamics of short range quantum critical fluctuations of incommensurate density wave order. Within hydrodynamics, pinned translational order is essential to obtain the nonzero frequency peak., Comment: 8+4+5 pages. 3 figures. v2: references added, discussion improved. v3: presentation revamped to emphasize main points. v4: minor tweaks to presentation and data points for more materials added. v5: minor revised version for SciPost

We apply the background field technique, recently developed for a general class of nonlinear symmetries, at tree level, to the Volkov-Akulov theory with spontaneously broken N=1 supersymmetry. We find that the background field expansion in terms of the free fields to the lowest order reproduces the nonlinear supersymmetry transformation rules. The double soft limit of the background field is, in agreement with the new general identities, defined by the algebra of the nonlinear symmetries., Comment: 10 p

We derive supersymmetry/supergravity models with constrained orthogonal nilpotent superfields from the linear models in the formal limit where the masses of the sgoldstino, inflatino and sinflaton tend to infinity. The case where the sinflaton mass remains finite leads to a model with a `relaxed' constraint, where the sinflaton remains an independent field. Our procedure is equivalent to a requirement that some of the components of the curvature of the moduli space tend to infinity., Comment: 18 pages, minor textual changes, small corrections, no conceptual changes. Added appendix C and extended appendix B

We derive a complete pure de Sitter supergravity action with non-linearly realized supersymmetry and its rigid limit, the Volkov-Akulov action, from the corresponding models with linear supersymmetry, by computing the path integral in the limit of infinite sgoldstino mass. In this, we use a non-Gaussian functional integration formula that was recently discovered in a derivation of de Sitter supergravity from the superconformal theory. We also present explicit examples of pure dS supergravity and the case with one matter multiplet. These two simple examples serve as a test and a demo of the universal action formula valid for de Sitter supergravities with general matter coupling., Comment: 15 pages

The ultraviolet divergences of amplitude diagrams in maximal supergravity are characterised by a first possible divergence at seven loops for the 4-point amplitude (logarithmic) and, in its absence, at eight loops. We revisit the pure spinor superfield theory results of [arXiv:1412.5983], stating the absence of the divergence originating in the 4-point 7-loop amplitude as well as those of more than seven loops. The analysis, performed in terms of the one-particle irreducible loop structures giving rise to the divergences, is extended, especially with respect to the limits on the dimension for finiteness. The results correspond to those mentioned, known from other approaches, indicating an ultraviolet finiteness of maximal supergravity in D=4., Comment: 28 pages, v2: Footnote added: further analysis required

The ultraviolet divergences of amplitude diagrams in maximal supergravity are investigated using the pure spinor superfield formalism in maximal supergravity, with maximally supersymmetric Yang-Mills theory for reference. We comment on the effects of the loop regularisation in relation to the actual absence of high powers (within the degrees of freedom) of the non-minimal variable r. The absence affects previous results of the field theory description, which is examined more closely (with a new b-ghost) with respect to the limit on the dimension for finiteness of the theory, dependent on the number of loops present. The results imply a cut-off of the loop dependence at six loops for the 4-point amplitude, and at seven loops otherwise., Comment: 28 pp. v3: Footnote added: further analysis required

We present a tensor calculus for exceptional generalised geometry. Expressions for connections, torsion and curvature are given a unified formulation for different exceptional groups E_n(n). We then consider "tensor gauge fields" coupled to the exceptional generalised gravity. Many of the properties of forms on manifolds are carried over to these fields., Comment: 22 pp., plain tex. v3: improved references

We present a description for amplitude diagrams in maximal supergravities obtained by dimensional reduction from D=11, derived from a field theory point of view using the pure spinor formalism. The advantages of this approach are the manifest supersymmetry present in the formalism, and the limited number of interaction terms in the action. Furthermore, we investigate the conditions set by this description in order for amplitudes in maximal supergravity to be finite in the ultraviolet limit. Typically, there is an upper limit to the dimension, set by the loop order, which for an arbitrary number of loops is no larger than two. In four dimensions, the non-renormalisation power of the formalism fails for the 7-loop contribution to the 4-point amplitude, all of which is in clear agreement with previous work., Comment: 53 pp. v2: refs. added

We present a method for introducing and analysing higher-derivative deformations of maximally supersymmetric field theories. Such terms are built in the pure spinor superfield framework, using a set of operators representing physical fields. The action for abelian Born-Infeld theory becomes polynomial in this language, and contains only a four-point interaction in addition to the free action. Simplifications also occur in the non-abelian case., Comment: 23 pp., plain tex