Regulating Eternal Inflation II: The Great Divide

In a previous paper, two of the authors presented a "regulated" picture of eternal inflation. This picture both suggested and drew support from a conjectured discontinuity in the amplitude for tunneling from positive to negative vacuum energy, as the positive vacuum energy was sent to zero; analytic and numerical arguments supporting this conjecture were given. Here we show that this conjecture is false, but in an interesting way. There are no cases where tunneling amplitudes are discontinuous at vanishing cosmological constant; rather, the space of potentials separates into two regions. In one region decay is strongly suppressed, and the proposed picture of eternal inflation remains viable; sending the (false) vacuum energy to zero in this region results in an absolutely stable asymptotically flat space. In the other region, we argue that the space-time at vanishing cosmological constant is unstable, but not asymptotically Minkowski. The consequences of our results for theories of supersymmetry breaking are unchanged.Comment: JHEP3, 19 Pages, 7 Figure

Out of equilibrium: understanding cosmological evolution to lower-entropy states

Despite the importance of the Second Law of Thermodynamics, it is not absolute. Statistical mechanics implies that, given sufficient time, systems near equilibrium will spontaneously fluctuate into lower-entropy states, locally reversing the thermodynamic arrow of time. We study the time development of such fluctuations, especially the very large fluctuations relevant to cosmology. Under fairly general assumptions, the most likely history of a fluctuation out of equilibrium is simply the CPT conjugate of the most likely way a system relaxes back to equilibrium. We use this idea to elucidate the spacetime structure of various fluctuations in (stable and metastable) de Sitter space and thermal anti-de Sitter space.Comment: 27 pages, 11 figure

Matrix Compactification On Orientifolds

Generalizing previous results for orbifolds, in this paper we describe the compactification of Matrix model on an orientifold which is a quotient space as a Yang-Mills theory living on a quantum space. The information of the compactification is encoded in the action of the discrete symmetry group G on Euclidean space and a projective representation U of G. The choice of Hilbert space on which the algebra of U is realized as an operator algebra corresponds to the choice of a physical background for the compactification. All these data are summarized in the spectral triple of the quantum space.Comment: 28 pages, late

Aspects of ALE Matrix Models and Twisted Matrix Strings

We examine several aspects of the formulation of M(atrix)-Theory on ALE spaces. We argue for the existence of massless vector multiplets in the resolved $A_{n-1}$ spaces, as required by enhanced gauge symmetry in M-Theory, and that these states might have the correct gravitational interactions. We propose a matrix model which describes M-Theory on an ALE space in the presence of wrapped membranes. We also consider orbifold descriptions of matrix string theories, as well as more exotic orbifolds of these models, and present a classification of twisted matrix string theories according to Reid's exact sequences of surface quotient singularities.Comment: 27 pages LaTeX2e, 7 figures, using utarticle.cls (included), array.sty, amsmath.sty, amsfonts.sty, cite.sty, epsf.sty. Bibtex style: utphys.bst (.bbl file included). Section on wrapped membrane states revised and expanded. We now argue for the existence of wrapped membranes and propose a matrix model which describes M-Theory on an ALE space in the presence of wrapped membrane

Black Holes and Five-brane Thermodynamics

The phase diagram for Dp-branes in M-theory compactified on $T^4$, $T^4/Z_2$, $T^5$, and $T^6$ is constructed. As for the lower-dimensional tori considered in our previous work (hep-th/9810224), the black brane phase at high entropy connects onto matrix theory at low entropy; we thus recover all known instances of matrix theory as consequences of the Maldacena conjecture. The difficulties that arise for $T^6$ are reviewed. We also analyze the D1-D5 system on $T^5$; we exhibit its relation to matrix models of M5-branes, and use spectral flow as a tool to investigate the dependence of the phase structure on angular momentum.Comment: 57 pages, 6 eps figures, latex. v2: DLCQ limit of 5-brane corrected; typos corrected, references added. v3: reference added, typos corrected v4: comments on DLCQ limit of 5-brane corrected one last time. Final version, to appear in Phys. Rev.

Black Holes and the Super Yang-Mills diagram. II

The complete phase diagram of objects in M-theory compactified on tori $T^p$, $p=1,2,3$, is elaborated. Phase transitions occur when the object localizes on cycle(s) (the Gregory-Laflamme transition), or when the area of the localized part of the horizon becomes one in string units (the Horowitz-Polchinski correspondence point). The low-energy, near-horizon geometry that governs a given phase can match onto a variety of asymptotic regimes. The analysis makes it clear that the matrix conjecture is a special case of the Maldacena conjecture.Comment: 23 pages, latex; 3 eps figures; v2: references and minor comments added. v3: reference adde

Extremal black holes as exact string solutions

We show that the leading order solution describing an extremal electrically charged black hole in string theory is, in fact, an exact solution to all orders in \a' when interpreted in a Kaluza-Klein fashion. This follows from the observation that it can be obtained via dimensional reduction from a five dimensional background which is proved to be an exact string solution.Comment: 13 pages, harvmac, Imperial/TP/93-94/51, UCSBTH-94-24 (references added

A status report on the observability of cosmic bubble collisions

In the picture of eternal inflation as driven by a scalar potential with multiple minima, our observable universe resides inside one of many bubbles formed from transitions out of a false vacuum. These bubbles necessarily collide, upsetting the homogeneity and isotropy of our bubble interior, and possibly leading to detectable signatures in the observable portion of our bubble, potentially in the Cosmic Microwave Background or other precision cosmological probes. This constitutes a direct experimental test of eternal inflation and the landscape of string theory vacua. Assessing this possibility roughly splits into answering three questions: What happens in a generic bubble collision? What observational effects might be expected? How likely are we to observe a collision? In this review we report the current progress on each of these questions, improve upon a few of the existing results, and attempt to lay out directions for future work.Comment: Review article; comments very welcome. 24 pages + 4 appendices; 19 color figures. (Revised version adds two figures, minor edits.

A Conformal Field Theory of a Rotating Dyon

A conformal field theory representing a four-dimensional classical solution of heterotic string theory is presented. The low-energy limit of this solution has U(1) electric and magnetic charges, and also nontrivial axion and dilaton fields. The low-energy metric contains mass, NUT and rotation parameters. We demonstrate that this solution corresponds to part of an extremal limit of the Kerr-Taub-NUT dyon solution. This limit displays interesting `remnant' behaviour, in that asymptotically far away from the dyon the angular momentum vanishes, but far down the infinite throat in the neighbourhood of the horizon (described by our CFT) there is a non-zero angular velocity. A further natural generalization of the CFT to include an additional parameter is presented, but the full physical interpretation of its role in the resulting low energy solution is unclear.Comment: 43 pages, Plain TEX + epsf.tex for one uuencoded figure

D-branes and Near Extremal Black Holes at Low Energies

It has been observed recently that many properties of some near extremal black holes can be described in terms of bound states of D-branes. Using a non-renormalization theorem we argue that the D-brane description is the correct quantum gravity description of the black hole at low energies. The low energy theory includes the black hole degrees of freedom that account for the entropy and describes also Hawking radiation. The description is unitary and there seems to be no information loss at low energies.Comment: 14 pages, 2 figures, uses harvmac, an error in a proof is corrected, the conclusions are the sam