Quantum geometry and gravitational entropy

Most quantum states have wavefunctions that are widely spread over the accessible Hilbert space and hence do not have a good description in terms of a single classical geometry. In order to understand when geometric descriptions are possible, we exploit the AdS/CFT correspondence in the half-BPS sector of asymptotically AdS_5 x S^5 universes. In this sector we devise a "coarse-grained metric operator" whose eigenstates are well described by a single spacetime topology and geometry. We show that such half-BPS universes have a non-vanishing entropy if and only if the metric is singular, and that the entropy arises from coarse-graining the geometry. Finally, we use our entropy formula to find the most entropic spacetimes with fixed asymptotic moments beyond the global charges.Comment: 29 pages, 2 figures; references adde

Polarizing Bubble Collisions

We predict the polarization of cosmic microwave background (CMB) photons that results from a cosmic bubble collision. The polarization is purely E-mode, symmetric around the axis pointing towards the collision bubble, and has several salient features in its radial dependence that can help distinguish it from a more conventional explanation for unusually cold or hot features in the CMB sky. The anomalous "cold spot" detected by the Wilkinson Microwave Anisotropy Probe (WMAP) satellite is a candidate for a feature produced by such a collision, and the Planck satellite and other proposed surveys will measure the polarization on it in the near future. The detection of such a collision would provide compelling evidence for the string theory landscape.Comment: Published version. 15 pages, 8 figure

Coarse-Graining the Lin-Maldacena Geometries

The Lin-Maldacena geometries are nonsingular gravity duals to degenerate vacuum states of a family of field theories with SU(2|4) supersymmetry. In this note, we show that at large N, where the number of vacuum states is large, there is a natural `macroscopic' description of typical states, giving rise to a set of coarse-grained geometries. For a given coarse-grained state, we can associate an entropy related to the number of underlying microstates. We find a simple formula for this entropy in terms of the data that specify the geometry. We see that this entropy function is zero for the original microstate geometries and maximized for a certain ``typical state'' geometry, which we argue is the gravity dual to the zero-temperature limit of the thermal state of the corresponding field theory. Finally, we note that the coarse-grained geometries are singular if and only if the entropy function is non-zero.Comment: 29 pages, LaTeX, 3 figures; v2 references adde

Can we detect Hot or Cold spots in the CMB with Minkowski Functionals?

In this paper, we investigate the utility of Minkowski Functionals as a probe of cold/hot disk-like structures in the CMB. In order to construct an accurate estimator, we resolve a long-standing issue with the use of Minkowski Functionals as probes of the CMB sky -- namely that of systematic differences ("residuals") when numerical and analytical MF are compared. We show that such residuals are in fact by-products of binning, and not caused by pixelation or masking as originally thought. We then derive a map-independent estimator that encodes the effects of binning, applicable to beyond our present work. Using this residual-free estimator, we show that small disk-like effects (as claimed by Vielva et al.) can be detected only when a large sample of such maps are averaged over. In other words, our estimator is noise-dominated for small disk sizes at WMAP resolution. To confirm our suspicion, we apply our estimator to the WMAP7 data to obtain a null result.Comment: 15 pages, 13 figure

1/4-BPS M-theory bubbles with SO(3) x SO(4) symmetry

In this paper we generalize the work of Lin, Lunin and Maldacena on the classification of 1/2-BPS M-theory solutions to a specific class of 1/4-BPS configurations. We are interested in the solutions of 11 dimensional supergravity with $SO(3)\times SO(4)$ symmetry, and it is shown that such solutions are constructed over a one-parameter familiy of 4 dimensional almost Calabi-Yau spaces. Through analytic continuations we can obtain M-theory solutions having $AdS_2\times S^3$ or $AdS_3\times S^2$ factors. It is shown that our result is equivalent to the $AdS$ solutions which have been recently reported as the near-horizon geometry of M2 or M5-branes wrapped on 2 or 4-cycles in Calabi-Yau threefolds. We also discuss the hierarchy of M-theory bubbles with different number of supersymmetries.Comment: 22 pages, JHEP3.cls; v2. revised version. showed that our results agree with previous works hep-th/0605146 and hep-th/061219

Bubble collisions and measures of the multiverse

To compute the spectrum of bubble collisions seen by an observer in an eternally-inflating multiverse, one must choose a measure over the diverging spacetime volume, including choosing an "initial" hypersurface below which there are no bubble nucleations. Previous calculations focused on the case where the initial hypersurface is pushed arbitrarily deep into the past. Interestingly, the observed spectrum depends on the orientation of the initial hypersurface, however one's ability observe the effect rapidly decreases with the ratio of inflationary Hubble rates inside and outside one's bubble. We investigate whether this conclusion might be avoided under more general circumstances, in particular placing the observer's bubble near the initial hypersurface. We find that it is not. As a point of reference, a substantial appendix reviews relevant aspects of the measure problem of eternal inflation.Comment: 24 pages, two figures, plus 16-page appendix with one figure; v2: minor improvements and clarifications, conclusions unchanged (version to appear in JCAP

Typicality versus thermality: An analytic distinction

In systems with a large degeneracy of states such as black holes, one expects that the average value of probe correlation functions will be well approximated by the thermal ensemble. To understand how correlation functions in individual microstates differ from the canonical ensemble average and from each other, we study the variances in correlators. Using general statistical considerations, we show that the variance between microstates will be exponentially suppressed in the entropy. However, by exploiting the analytic properties of correlation functions we argue that these variances are amplified in imaginary time, thereby distinguishing pure states from the thermal density matrix. We demonstrate our general results in specific examples and argue that our results apply to the microstates of black holes.Comment: 22 pages + appendices, 3 eps figure

Black Holes as Effective Geometries

Gravitational entropy arises in string theory via coarse graining over an underlying space of microstates. In this review we would like to address the question of how the classical black hole geometry itself arises as an effective or approximate description of a pure state, in a closed string theory, which semiclassical observers are unable to distinguish from the "naive" geometry. In cases with enough supersymmetry it has been possible to explicitly construct these microstates in spacetime, and understand how coarse-graining of non-singular, horizon-free objects can lead to an effective description as an extremal black hole. We discuss how these results arise for examples in Type II string theory on AdS_5 x S^5 and on AdS_3 x S^3 x T^4 that preserve 16 and 8 supercharges respectively. For such a picture of black holes as effective geometries to extend to cases with finite horizon area the scale of quantum effects in gravity would have to extend well beyond the vicinity of the singularities in the effective theory. By studying examples in M-theory on AdS_3 x S^2 x CY that preserve 4 supersymmetries we show how this can happen.Comment: Review based on lectures of JdB at CERN RTN Winter School and of VB at PIMS Summer School. 68 pages. Added reference

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.

Genome-wide Analysis of STAT3-Mediated Transcription during Early Human Th17 Cell Differentiation

The development of therapeutic strategies to combat immune-associated diseases requires the molecular mechanisms of human Th17 cell differentiation to be fully identified and understood. To investigate transcriptional control of Th17 cell differentiation, we used primary human CD4+ T cells in small interfering RNA (siRNA)-mediated gene silencing and chromatin immunoprecipitation followed by massive parallel sequencing (ChIP-seq) to identify both the early direct and indirect targets of STAT3. The integrated dataset presented in this study confirms that STAT3 is critical for transcriptional regulation of early human Th17 cell differentiation. Additionally, we found that a number of SNPs from loci associated with immune-mediated disorders were located at sites where STAT3 binds to induce Th17 cell specification. Importantly, introduction of such SNPs alters STAT3 binding in DNA affinity precipitation assays. Overall, our study provides important insights for modulating Th17-mediated pathogenic immune responses in humans.</p