Generalized Conformal Symmetry and Oblique AdS/CFT Correspondence for Matrix Theory

The large N behavior of Matrix theory is discussed on the basis of the previously proposed generalized conformal symmetry. The concept of `oblique' AdS/CFT correspondence, in which the conformal symmetry involves both the space-time coordinates and the string coupling constant, is proposed. Based on the explicit predictions for two-point correlators, possible implications for the Matrix-theory conjecture are discussed.Comment: LaTeX, 10 pages, 2 figures, written version of the talk presented at Strings'9

Fast Scramblers, Horizons and Expander Graphs

We propose that local quantum systems defined on expander graphs provide a simple microscopic model for thermalization on quantum horizons. Such systems are automatically fast scramblers and are motivated from the membrane paradigm by a conformal transformation to the so-called optical metric.Comment: 22 pages, 2 figures. Added further discussion in section 3. Added reference

Anisotropic scale invariant cosmology

We study a possibility of anisotropic scale invariant cosmology. It is shown that within the conventional Einstein gravity, the violation of the null energy condition is necessary. We construct an example based on a ghost condensation model that violates the null energy condition. The cosmological solution necessarily contains at least one contracting spatial direction as in the Kasner solution. Our cosmology is conjectured to be dual to, if any, a non-unitary anisotropic scale invariant Euclidean field theory. We investigate simple correlation functions of the dual theory by using the holographic computation. After compactification of the contracting direction, our setup may yield a dual field theory description of the winding tachyon condensation that might solve the singularity of big bang/crunch of the universe.Comment: 12 pages, v2: reference adde

Fast Scramblers Of Small Size

We investigate various geometrical aspects of the notion of `optical depth' in the thermal atmosphere of black hole horizons. Optical depth has been proposed as a measure of fast-crambling times in such black hole systems, and the associated optical metric suggests that classical chaos plays a leading role in the actual scrambling mechanism. We study the behavior of the optical depth with the size of the system and find that AdS/CFT phase transitions with topology change occur naturally as the scrambler becomes smaller than its thermal length. In the context of detailed AdS/CFT models based on D-branes, T-duality implies that small scramblers are described in terms of matrix quantum mechanics.Comment: 14 pages, 3 figures. Added reference

Nonlocality vs. complementarity: a conservative approach to the information problem

A proposal for resolution of the information paradox is that "nice slice" states, which have been viewed as providing a sharp argument for information loss, do not in fact do so as they do not give a fully accurate description of the quantum state of a black hole. This however leaves an information *problem*, which is to provide a consistent description of how information escapes when a black hole evaporates. While a rather extreme form of nonlocality has been advocated in the form of complementarity, this paper argues that is not necessary, and more modest nonlocality could solve the information problem. One possible distinguishing characteristic of scenarios is the information retention time. The question of whether such nonlocality implies acausality, and particularly inconsistency, is briefly addressed. The need for such nonlocality, and its apparent tension with our empirical observations of local quantum field theory, may be a critical missing piece in understanding the principles of quantum gravity.Comment: 11 pages of text and figures, + references. v2 minor text. v3 small revisions to match final journal versio

No Forbidden Landscape in String/M-theory

Scale invariant but non-conformal field theories are forbidden in (1+1) dimension, and so should be the corresponding holographic dual gravity theories. We conjecture that such scale invariant but non-conformal field configurations do not exist in the string/M-theory. We provide a proof of this conjecture in the classical supergravity limit under a certain gauge condition. Our proof does also apply in higher dimensional scale invariant but non-conformal field configurations, which suggests that scale invariant but non-conformal field theories may be forbidden in higher dimensions as well.Comment: 14 pages, v2: energy condition on c-theorem is corrected, v3: extra assumption in the proof is discussed due to a sign error in the previous versio

Brownian motion in AdS/CFT

We study Brownian motion and the associated Langevin equation in AdS/CFT. The Brownian particle is realized in the bulk spacetime as a probe fundamental string in an asymptotically AdS black hole background, stretching between the AdS boundary and the horizon. The modes on the string are excited by the thermal black hole environment and consequently the string endpoint at the boundary undergoes an erratic motion, which is identified with an external quark in the boundary CFT exhibiting Brownian motion. Semiclassically, the modes on the string are thermally excited due to Hawking radiation, which translates into the random force appearing in the boundary Langevin equation, while the friction in the Langevin equation corresponds to the excitation on the string being absorbed by the black hole. We give a bulk proof of the fluctuation-dissipation theorem relating the random force and friction. This work can be regarded as a step toward understanding the quantum microphysics underlying the fluid-gravity correspondence. We also initiate a study of the properties of the effective membrane or stretched horizon picture of black holes using our bulk description of Brownian motion.Comment: 54 pages (38 pages + 5 appendices), 5 figures. v2: references added, clarifications in 6.2. v3: clarifications, version submitted to JHE

Can the Horowitz-Maldacena proposal be an alternative to the firewall?

Recently, there have been discussions that black hole complementarity is inconsistent and that the firewall is required to prohibit the observation of duplicated information. It is thought that if the Horowitz-Maldacena proposal works as a selection principle, then this may be an alternative to the firewall. In this paper, we first point out that the Horowitz-Maldacena proposal seems to help black hole complementarity for charged black holes. However, if we consider the Hayden-Preskill argument further, which states that a black hole can function as an information mirror after the information retention time, then we can show that the Horowitz-Maldaceana proposal cannot help black hole complementarity. This can be extended to neutral black hole cases. Therefore, in conclusion, we find that dynamical black holes do not respect complementarity, even with the Horowitz-Maldacena proposal.Comment: 11 pages, 3 figure

Membrane paradigm realized?

Are there any degrees of freedom on the black hole horizon? Using the `membrane paradigm' we can reproduce coarse-grained physics outside the hole by assuming a fictitious membrane just outside the horizon. But to solve the information puzzle we need `real' degrees of freedom at the horizon, which can modify Hawking's evolution of quantum modes. We argue that recent results on gravitational microstates imply a set of real degrees of freedom just outside the horizon; the state of the hole is a linear combination of rapidly oscillating gravitational solutions with support concentrated just outside the horizon radius. The collective behavior of these microstate solutions may give a realization of the membrane paradigm, with the fictitious membrane now replaced by real, explicit degrees of freedom.Comment: 8 pages, Latex, 3 figures (Essay given second place in Gravity Research Foundation essay competition 2010

Condensation of an ideal gas with intermediate statistics on the horizon

We consider a boson gas on the stretched horizon of the Schwartzschild and Kerr black holes. It is shown that the gas is in a Bose-Einstein condensed state with the Hawking temperature $T_c=T_H$ if the particle number of the system be equal to the number of quantum bits of space-time N \simeq {A}/{{\l_{p}}^{2}}. Entropy of the gas is proportional to the area of the horizon $(A)$ by construction. For a more realistic model of quantum degrees of freedom on the horizon, we should presumably consider interacting bosons (gravitons). An ideal gas with intermediate statistics could be considered as an effective theory for interacting bosons. This analysis shows that we may obtain a correct entropy just by a suitable choice of parameter in the intermediate statistics.Comment: 12 pages, added new sections related to an ideal gas with intermediate statistic