Abstract:We analyze various aspects of the recently proposed holographic theories with general dynamical critical exponent z and hyperscaling violation exponent θ. We first find the basic constraints on z, θ from the gravity side, and compute the stress-energy tensor expectation values and scalar two-point functions. Massive correlators exhibit a nontrivial exponential behavior at long distances, controlled by θ. At short distance, the two-point functions become power-law, with a universal form for θ > 0. Next, the calculation of the holographic entanglement entropy reveals the existence of novel phases which violate the area law. The entropy in these phases has a behavior that interpolates between that of a Fermi surface and that exhibited by systems with extensive entanglement entropy. Finally, we describe microscopic embeddings of some θ = 0 metrics into full string theory models -these metrics characterize large regions of the parameter space of Dp-brane metrics for p = 3. For instance, the theory of N D2-branes in IIA supergravity has z = 1 and θ = −1/3 over a wide range of scales, at large g s N .
We compute the modular Hamiltonians of regions having the future horizon lying on a null plane. For a CFT this is equivalent to regions with boundary of arbitrary shape lying on the null cone. These Hamiltonians have a local expression on the horizon formed by integrals of the stress tensor. We prove this result in two different ways, and show that the modular Hamiltonians of these regions form an infinite dimensional Lie algebra. The corresponding group of unitary transformations moves the fields on the null surface locally along the null generators with arbitrary null line dependent velocities, but act non locally outside the null plane. We regain this result in greater generality using more abstract tools on algebraic quantum field theory. Finally, we show that modular Hamiltonians on the null surface satisfy a Markov property that leads to the saturation of the strong sub-additive inequality for the entropies and to the strong super-additivity of the relative entropy.
The TT deformation of a conformal field theory has a dual description as a cutoff AdS 3 spacetime, at least at the level of pure 3d gravity. We generalize this deformation in such a way that it builds up a patch of bulk dS 3 spacetime instead. At each step along the trajectory in the space of 2d theories, the theory is deformed by a specific combination of TT and the two-dimensional cosmological constant. This provides a concrete holographic dual for the warped throat on the gravity side of the dS/dS duality, at leading order in large central charge. We also analyze a sequence of excitations of this throat on both sides of the duality, as well as the entanglement entropy. Our results point toward a mechanism for obtaining de Sitter solutions starting from seed conformal field theories with AdS duals.
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