The emergent nature of spacetime geometry and black holes can be directly probed in simple holographic duals of higher spin gravity and tensionless string theory. To this end, we study time dependent thermal correlation functions of gauge invariant observables in suitably chosen free large N gauge theories. At low temperature and on short time scales the correlation functions encode propagation through an approximate AdS spacetime while interesting departures emerge at high temperature and on longer time scales. This includes the existence of evanescent modes and the exponential decay of time dependent boundary correlations, both of which are well known indicators of bulk black holes in AdS/CFT. In addition, a new time scale emerges after which the correlation functions return to a bulk thermal AdS form up to an overall temperature dependent normalization. A corresponding length scale was seen in equal time correlation functions in the same models in our earlier work.

Boundary correlation functions provide insight into the emergence of an effective geometry in higher spin gravity duals of O(N) or U(N) symmetric field theories. On a compact manifold, the singlet constraint leads to nontrivial dynamics at finite temperature and large N phase transitions even at vanishing 't Hooft coupling. At low temperature, the leading behavior of boundary two-point functions is consistent with propagation through a bulk thermal anti de Sitter space. Above the phase transition, the two-point function shows significant departure from thermal AdS space and the emergence of localized black hole like objects in the bulk. In adjoint models, these objects appear at length scales of order of the AdS radius, consistent with a Hawking-Page transition, but in vector models they are parametrically larger than the AdS scale. In low dimensions, we find another crossover at large distances beyond which the correlation function again takes a thermal AdS form, albeit with a temperature dependent normalization factor.

We suggest that holography can be formulated in terms of the information capacity of the Stuckelberg degrees of freedom that maintain gauge invariance of the theory in the presence of an information boundary. These Stuckelbergs act as qubits that account for a certain fraion of quantum information. Their information capacity is measured by the ratio of the inverse Stuckeerg energy gap to the size of the syste. Systems with the smallest gap are maximally holographic. For massless gauge systems this information measure is universally equal to the inverse coupling evaluated at the systems' length scale. In this language it becomes very transparent why the Stuckelberg informatn capacity of black holes saturates the Bekenstein bound and accounts for the entire information of the system. The physical reason is that the strength of quantum interaction is bounded from below by the gravitational coupling, which scales as area. Observing the striking similarity between the scalings of the energy gap of the boundary Stuckelbe modes and the Bogoliubov modes of critical my -body systems, we establish a connection between holography and quantum criticality through the correspondence between these modes.

We establish a fundamental connection between quantum criticality of a many-body system, such as Bose-Einstein condensates, and its capacity of information-storage and processing. For deriving the effective theory of modes in the vicinity of the quantum critical point, we develop a new method by mapping a Bose-Einstein condensate of N-particles onto a sigma model with a continuous global (pseudo) symmetry that mixes bosons of different momenta. The Bogolyubov modes of the condensate are mapped onto the Goldstone modes of the sigma model, which become gapless at the critical point. These gapless Goldstone modes are the quantum carriers of information and entropy. Analyzing their effective theory, we observe information-processing properties strikingly similar to the ones predicted by the black hole portrait. The energy cost per qubit of information-storage vanishes in the large-N limit and the total information-storage capacity increases with N either exponentially or as a power law. The longevity of information-storage also increases with N, whereas the scrambling time in the over-critical regime is controlled by the Lyapunov exponent and scales logarithmically with N. This connection reveals that the origin of black hole information storage lies in the quantum criticality of the graviton Bose-gas, and that much simpler systems that can be manufactured in table-top experiments can exhibit very similar information-processing dynamics.

We investigate Hawking evaporation in a recently suggested picture in which black holes are Bose condensates of gravitons at a quantum critical point. There, evaporation of a black hole is due to two intertwined effects. Coherent excitation of a tachyonic breathing mode is responsible for the collapse of the condensate, while incoherent scattering of gravitons leads to Hawking radiation. To explore this, we consider a toy model of a single bosonic degree of freedom with derivative self-interactions. We consider the real-time evolution of a condensate and derive evaporation laws for two possible decay mechanisms in the Schwinger-Keldysh formalism. We show that semiclassical results can be reproduced if the decay is due to an effective two-body process, while the existence of a three-body channel would imply very short lifetimes for the condensate. In either case, we uncover the existence of scaling solutions in which the condensate is at a critical point throughout the collapse. In the case of a two-body decay we moreover discover solutions that exhibit the kind of instability that was recently conjectured to be responsible for fast scrambling.