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 super gravity has z = 1 and θ = −1/3 over a wide range of scales, at large g
 s
 N.

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Aspects of holography for theories with hyperscaling violation

We give a broad conceptual review of what we have learned about black holes and their microstate structure from the study of microstate geometries and their string theory limits. We draw upon general relativity, supergravity, string theory and holographic field theory to extract universal ideas and structural features that we expect to be important in resolving the information problem and understanding the microstate structure of Schwarzschild and Kerr black holes. In particular, we emphasize two conceptually and physically distinct ideas, with different underlying energy scales: a) the transition that supports the microstate structure and prevents the formation of a horizon and b) the representation of the detailed microstate structure itself in terms of fluctuations around the transitioned state. We also show that the supergravity mechanism that supports microstate geometries becomes, in the string theory limit, either brane polarization or the excitation of non-Abelian degrees of freedom. We thus argue that if any mechanism for supporting structure at the horizon scale is to be given substance within string theory then it must be some manifestation of microstate geometries.

Resolving the Structure of Black Holes: Philosophizing with a Hammer

Depending on the value of the coupling, BPS states of type II string the- ory compactied on a Calabi-Yau manifold can be described as multicenter supergravity solutions or as BPS states in a quiver gauge theory. While states that spread into the Coulomb-branch states can be mapped one-to-one to supergravity states, this is not auto- matically so for the majority of Higgs-branch states. In this paper we explicitly compute the BPS spectrum of the Higgs branch of a three-center quiver with a closed loop, and iden- tify the subset of states that are in one-to-one correspondence with Coulomb/supergravity multicenter states. We also show that there exist additional \pure-Higgs" states, that exist if and only if the charges of the centers can form a scaling solution. Using generating function techniques we compute the large charge degeneracy of the \pure-Higgs" sector and show that it is always exponential. We also construct the map between Higgs- and Coulomb-branch states, discuss its relation to the Higgs-Coulomb map of one of the authors and Verlinde, and argue that the pure Higgs states live in the kernel of this map. Given that these states have no obvious description on the Coulomb branch or in supergravity, we discuss whether they can correspond to a single-center black hole or can be related to more complicated horizonless congurations.

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Scaling BPS solutions and pure-Higgs states

Euclidean wormholes---geometries which connect disconnected boundaries---present a challenge to a standard quantum mechanical interpretation of the theory. One potential resolution is that the gravitational path integral computes the ensemble average of many theories. The connected topologies contribute to the simplest possible observable: the free energy, which is computed using a replica trick. This is distinct from the replica trick used to compute entanglement entropies and appears in the computation of any extensive quantity. We argue that both JT gravity and a simplified version of CGHS admit a regime where the contribution of connected replica wormholes to the free energy is larger than that of disconnected topologies. In both theories we find evidence of replica symmetry breaking, which is reminiscent of the behavior of certain spin glasses. We discuss possible insights about ensemble averaging in gravity from this perspective.

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Free Energy from Replica Wormholes

We analyze the low temperature structure of a supersymmetric quiver quantum mechanics with randomized superpotential coefficients, treating them as quenched disorder. These theories describe features of the low energy dynamics of wrapped branes, which in large number backreact into extremal black holes. We show that the low temperature theory, in the limit of a large number of bifundamentals, exhibits a time reparametrization symmetry as well as a specific heat linear in the temperature. Both these features resemble the behavior of black hole horizons in the zero temperature limit. We demonstrate similarities between the low temperature physics of the random quiver model and a theory of large N free fermions with random masses.

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Disordered quivers and cold horizons

We initiate a systematic study of the state space of non-extremal, stationary black hole bound states in four-dimensional N = 2 supergravity. Specifically, we show that an exponential multitude of classically stable "halo" bound states can be formed between large finite temperature D4-D0 black hole cores and much smaller, arbitrarily charged black holes at the same temperature. We map out in full the regions of existence for thermodynamically stable and metastable bound states in terms of the core's charges and temperature, as well as the region of stability of the core itself. Several features of these systems, such as a macroscopic configurational entropy and exponential relaxation timescales, are similar to those of the extended family of glasses. We draw parallels between the two with a view toward understanding complex systems in fundamental physics.

Hot Halos and Galactic Glasses

We initiate a systematic study of the state space of non-extremal, stationary black hole bound states in four-dimensional $ \mathcal{N} = {2} $
 supergravity. Specifically, we show that an exponential multitude of classically stable “halo” bound states can be formed between large finite temperature D4-D0 black hole cores and much smaller, arbitrarily charged black holes at the same temperature. We map out in full the regions of existence for thermodynamically stable and metastable bound states in terms of the core’s charges and temperature, as well as the region of stability of the core itself. Several features of these systems, such as a macroscopic configurational entropy and exponential relaxation timescales, are similar to those of the extended family of glasses. We draw parallels between the two with a view toward understanding complex systems in fundamental physics.

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Hot Halos and Galactic Glasses (Carbonado)

We discuss the existence of scaling solutions for multicenter black hole configurations. One of the central results is the equivalence between the existence of two centered scaling solutions and the holographic entropy bound. This equivalence (and another one) are proved rigorously at the end of the paper, and allow to simplify the process counting of certain (fuzzball-like) contributions to black hole entropy.

Bram Gaasbeek

Papers

Hot Halos and Galactic Glasses

Hot Halos and Galactic Glasses (Carbonado)

A holographic bound on the scaling contribution to black hole entropy