Brett McInnes

The phantom divide in string gas cosmology

Abstract One of the main virtues of string gas cosmology is that it resolves cosmological singularities. Since the Universe can be approximated by a locally asymptotically de Sitter spacetime by the end of the inflationary era, a singularity theorem implies that these cosmologies effectively violate the Null Energy Condition (not just the Strong Energy Condition). We stress that this is an extremely robust result, which does not depend on assuming that the spatial sections remain precisely flat in the early Universe. This means, however, that it must be possible for string cosmologies to cross the recently much-discussed phantom divide (from w − 1 to w > − 1 , where w is the equation-of-state parameter). This naturally raises the question as to whether the phantom divide can be crossed again, to account for recent observations suggesting that w − 1 at the present time. We argue that non-perturbative string effects rule out this possibility, even if the NEC violation in question is only “effective”.

Bounding the temperatures of black holes dual to strongly coupled field theories on flat spacetime

We show that AdS black holes dual to field theories on flat spacetime, as used in applications of the AdS/CFT correspondence to strong interaction and condensed matter physics, have temperatures with positive lower bounds. There are two distinct effects involved. For low chemical potentials in the dual field theory, the cooling black hole makes a transition to a state corresponding to confinement in the field theory. For high chemical potentials, it becomes unstable to a non-perturbative string effect. This allows a holographic sketch of the field theory phase diagram, one which is in qualitative agreement with the phenomenological understanding of the theory at [relatively] low temperatures. It also puts an interesting upper bound on the temperature-normalized chemical potential of the field theory, if it describes a plasma: in the normalization of Myers et al., must be less than approximately 0.49. Thus, the extent to which a chemical potential can worsen violations of the KSS bound is severely restricted.

Quintessential Maldacena-Maoz cosmologies

Maldacena and Maoz have proposed a new approach to holographic cosmology based on euclidean manifolds with disconnected boundaries. This approach appears, however, to be in conflict with the known geometric results (the Witten-Yau theorem and its extensions) on spaces with boundaries of non-negative scalar curvature. We show precisely how the Maldacena-Maoz approach evades these theorems. We also exhibit Maldacena-Maoz cosmologies with (cosmologically) more natural matter content, namely quintessence instead of Yang-Mills fields, thereby demonstrating that these cosmologies do not depend on a special choice of matter to split the euclidean boundary. We conclude that if our Universe is fundamentally anti-de Sitter-like (with the current acceleration being only temporary), then this may force us to confront the holography of spaces with a connected bulk but a disconnected boundary.

Black Hole Final State Conspiracies

Abstract The principle that unitarity must be preserved in all processes, no matter how exotic, has led to deep insights into boundary conditions in cosmology and black hole theory. In the case of black hole evaporation, Horowitz and Maldacena were led to propose that unitarity preservation can be understood in terms of a restriction imposed on the wave function at the singularity. Gottesman and Preskill showed that this natural idea only works if one postulates the presence of “conspiracies” between systems just inside the event horizon and states at much later times, near the singularity. We argue that some AdS black holes have unusual internal thermodynamics, and that this may permit the required “conspiracies” if real black holes are described by some kind of sum over all AdS black holes having the same entropy.

Methods of holonomy theory for Ricci‐flat Riemannian manifolds

Compact, Ricci‐flat Riemannian manifolds often arise in physical applications, either as a technical device or as models of ‘‘internal’’ space. The idea of extending the holonomy group of such a manifold to a larger gauge group (‘‘embedding the connection in the gauge group’’) plays a fundamental role in the ‘‘manifold compactification’’ approach to superstring phenomenology, and the work of Gepner suggests that this idea may have equally fundamental analogs in other approaches. The holonomy theory of simply connected Ricci‐flat manifolds has recently been the subject of much mathematical work, but physicists are mainly interested in the case of multiply connected manifolds. The purpose of this paper is to present some techniques for understanding the holonomy theory of compact, multiply connected Ricci‐flat manifolds. These lead to a general classification theorem.

Generalized planar black holes and the holography of hydrodynamic shear

Abstract AdS black holes with planar event horizon topology play a central role in AdS/CFT holography, and particularly in its applications. Generalizations of the known planar black holes can be found by considering the Plebanski–Demianski metrics, a very general family of exactly specified solutions of the Einstein equations. These generalized planar black holes may be useful in applications. We give a concrete example of this in the context of the holographic description of the Quark–Gluon Plasma (QGP). We argue that our generalized planar black holes allow us to construct a model of the internal shearing motion generated when the QGP is produced in peripheral heavy-ion collisions. When embedded in string theory, the bulk physics is in fact unstable. We find however that this instability may develop too slowly to affect the evolution of the plasma, except possibly for high values of the quark chemical potential, such as will be studied in experimental scans of the quark matter phase diagram.

Orbifold physics and de Sitter spacetime

Abstract It is generally believed the way to resolve the black hole information paradox in string theory is to embed the black hole in anti-de Sitter spacetime— without of course claiming that Schwarzschild-AdS is a realistic spacetime. Here we propose that, similarly, the best way to study topologically non-trivial versions of de Sitter spacetime from a stringy point of view is to embed them in an anti-de Sitter orbifold bulk, again without claiming that this is literally how de Sitter arises in string theory. Our results indicate that string theory may rule out the more complex spacetime topologies which are compatible with local de Sitter geometry, while still allowing the simplest versions.

Arrow of time in string theory

Abstract Inflation allows the problem of the arrow of time to be understood as a question about the structure of spacetime: why was the intrinsic curvature of the earliest spatial sections so much better behaved than it might have been? This is really just the complement of a more familiar problem: what mechanism prevents the extrinsic curvature of the earliest spatial sections from diverging, as classical general relativity suggests? We argue that the stringy version of “creation from nothing”, sketched by Ooguri, Vafa, and Verlinde, solves both of these problems at once. The argument, while very simple, hinges on some of the deepest theorems in global differential geometry. These results imply that when a spatially toral spacetime is created from nothing, the earliest spatial sections are forced to be [quasi-classically] exactly locally isotropic. This local isotropy, in turn, forces the inflaton into its minimal-entropy state. The theory explains why the arrow does not reverse in black holes or in a cosmic contraction, if any.

When Is Holography Consistent

Holographic duality relates two radically different kinds of theory: one with gravity, one without. The very existence of such an equivalence imposes strong consistency conditions which are, in the nature of the case, hard to satisfy. Recently a particularly deep condition of this kind, relating the minimum of a probe brane action to a gravitational bulk action (in a Euclidean formulation), has been recognized; and the question arises as to the circumstances under which it, and its Lorentzian counterpart, is satisfied. We discuss the fact that there are physically interesting situations in which one or both versions might, in principle, not be satisfied. These arise in two distinct circumstances: first, when the bulk is not an Einstein manifold and, second, in the presence of angular momentum. Focusing on the application of holography to the quark–gluon plasma (of the various forms arising in the early Universe and in heavy-ion collisions), we find that these potential violations never actually occur. This suggests that the consistency condition is a “law of physics” expressing a particular aspect of holography.

Angular Momentum in QGP Holography

Abstract The quark chemical potential is one of the fundamental parameters describing the quark–gluon plasma produced by sufficiently energetic heavy-ion collisions. It is not large at the extremely high temperatures probed by the LHC, but it plays a key role in discussions of the beam energy scan programmes at the RHIC and other facilities. On the other hand, collisions at such energies typically (that is, in peripheral collisions) give rise to very high values of the angular momentum density. Here we explain that holographic estimates of the quark chemical potential of a rotating sample of plasma can be very considerably improved by taking the angular momentum into account.