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Register a new userHolographic Quantum Statistics from Dual Thermodynamics
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We propose dual thermodynamics corresponding to black hole mechanics with the identifications E -> A/4, S -> M, and T -> 1/T in Planck units. Here A, M and T are the horizon area, mass and Hawking temperature of a black hole and E, S and T are the energy, entropy and temperature of a corresponding dual quantum system. We show that, for a Schwarzschild black hole, the dual variables formally satisfy all three laws of thermodynamics, including the Planck-Nernst form of the third law requiring that the entropy tend to zero at low temperature. This is in contrast with traditional black hole thermodynamics, where the entropy is singular. Once the third law is satisfied, it is straightforward to construct simple (dual) quantum systems representing black hole mechanics. As an example, we construct toy models from one dimensional (Fermi or Bose) quantum gases with N ~ M in a Planck scale box. In addition to recovering black hole mechanics, we obtain quantum corrections to the entropy, including the logarithmic correction obtained by previous papers. The energy-entropy duality transforms a strongly interacting gravitational system (black hole) into a weakly interacting quantum system (quantum gas) and thus provides a natural framework for the quantum statistics underlying the holographic conjecture.
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In this paper, we will analyze the connection between the fidelity susceptibility, the holographic complexity and the thermodynamic volume. We will regularize the fidelity susceptibility and the holographic complexity by subtracting the contribution of the background AdS spacetime from the deformation of the AdS spacetime. It will be demonstrated that this regularized fidelity susceptibility has the same behavior as the thermodynamic volume and that the regularized complexity has a very different behavior. As the information dual to different volumes in the bulk would be measured by the fidelity susceptibility and the holographic complexity, this paper will establish a connection between thermodynamics and information dual to a volume.
We define bulk/boundary maps corresponding to quantum gravity states in the tensorial group field theory formalism, for quantum geometric models sharing the same type of quantum states of loop quantum gravity. The maps are defined in terms of a partition of the quantum geometric data associated to an open graph into bulk and boundary ones, in the spin representation. We determine the general condition on the entanglement structure of the state that makes the bulk/boundary map isometric (a necessary condition for holographic behaviour), and we analyse different types of quantum states, identifying those that define isometric bulk/boundary maps.
We consider the holographic duality between type-A higher-spin gravity in AdS_4 and the free U(N) vector model. In the bulk, linearized solutions can be translated into twistor functions via the Penrose transform. We propose a holographic dual to this transform, which translates between twistor functions and CFT sources and operators. We present a twistorial expression for the partition function, which makes global higher-spin symmetry manifest, and appears to automatically include all necessary contact terms. In this picture, twistor space provides a fully nonlocal, gauge-invariant description underlying both bulk and boundary spacetime pictures. While the bulk theory is handled at the linear level, our formula for the partition function includes the effects of bulk interactions. Thus, the CFT is used to solve the bulk, with twistors as a language common to both. A key ingredient in our result is the study of ordinary spacetime symmetries within the fundamental representation of higher-spin algebra. The object that makes these square root spacetime symmetries manifest becomes the kernel of our boundary/twistor transform, while the original Penrose transform is identified as a square root of CPT.
We construct a generalized Smarr formula which could provide a thermodynamic route to derive the covariant field equation of general theories of gravity in dynamic spacetimes. Combining some thermodynamic variables and a new chemical potential conjugated to the number of degree of freedom on the holographic screen, we find a universal Cardy-Verlinde formula and give its braneworld interpretation. We demonstrate that the associated AdS-Bekenstein bound is tighten than the previous expression for multi-charge black holes in the gauged supergravities. The Cardy-Verlinde formula and the AdS-Bekenstein bound are derived from the thermodynamics of bulk trapping horizons, which strongly suggests the underlying holographic duality between dynamical bulk spacetime and boundary field theory.
The formalism of Holographic Space-time (HST) is a translation of the principles of Lorentzian geometry into the language of quantum information. Intervals along time-like trajectories, and their associated causal diamonds, completely characterize a Lorentzian geometry. The Bekenstein-Hawking-Gibbons-t Hooft-Jacobson-Fischler-Susskind-Bousso Covariant Entropy Principle, equates the logarithm of the dimension of the Hilbert space associated with a diamond to one quarter of the area of the diamonds holographic screen, measured in Planck units. The most convincing argument for this principle is Jacobsons derivation of Einsteins equations as the hydrodynamic expression of this entropy law. In that context, the null energy condition (NEC) is seen to be the analog of the local law of entropy increase. The quantum version of Einsteins relativity principle is a set of constraints on the mutual quantum information shared by causal diamonds along different time-like trajectories. The implementation of this constraint for trajectories in relative motion is the greatest unsolved problem in HST. The other key feature of HST is its claim that, for non-negative cosmological constant or causal diamonds much smaller than the asymptotic radius of curvature for negative c.c., the degrees of freedom localized in the bulk of a diamond are constrained states of variables defined on the holographic screen. This principle gives a simple explanation of otherwise puzzling features of BH entropy formulae, and resolves the firewall problem for black holes in Minkowski space. It motivates a covariant version of the CKNcite{ckn} bound on the regime of validity of quantum field theory (QFT) and a detailed picture of the way in which QFT emerges as an approximation to the exact theory.
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