Exotic polarizations of D2 branes and oblique vacua of (S)YM2+1_{2+1}

We investigate the oblique vacua in the perturbed 2+1 dimensional gauge theory living on D2 branes. The string theory dual of these vacua is expected to correspond to polarizations of the D2 branes into NS5 branes with D4 brane charge. We perturb the gauge theory by adding fermions masses. In the nonsupersymmetric case, we also consider the effect of slight variations of the masses of the scalars. For certain ranges of scalar masses we find oblique vacua. We show that D4 charge is an essential ingredient in understanding D2 -> NS5 polarizations. We find that some of the polarization states which appear as metastable vacua when D4 charge is not considered are in fact unstable. They decay by acquiring D4 charge, tilting and shrinking to zero size.Comment: 15 pages, 3 figures, LaTe

What we don't know about time

String theory has transformed our understanding of geometry, topology and spacetime. Thus, for this special issue of Foundations of Physics commemorating "Forty Years of String Theory", it seems appropriate to step back and ask what we do not understand. As I will discuss, time remains the least understood concept in physical theory. While we have made significant progress in understanding space, our understanding of time has not progressed much beyond the level of a century ago when Einstein introduced the idea of space-time as a combined entity. Thus, I will raise a series of open questions about time, and will review some of the progress that has been made as a roadmap for the future.Comment: 15 pages; Essay for a special issue of Foundations of Physics commemorating "Forty years of string theory

On the existence of supergravity duals to D1--D5 CFT states

We define a metric operator in the 1/2-BPS sector of the D1-D5 CFT, the eigenstates of which have a good semi-classical supergravity dual; the non-eigenstates cannot be mapped to semi-classical gravity duals. We also analyse how the data defining a CFT state manifests itself in the gravity side, and show that it is arranged into a set of multipoles. Interestingly, we find that quantum mechanical interference in the CFT can have observable manifestations in the semi-classical gravity dual. We also point out that the multipoles associated to the normal statistical ensemble fluctuate wildly, indicating that the mixed thermal state should not be associated to a semi-classical geometry.Comment: 22 pages, 2 figures. v2 : references added, typos correcte

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

Anatomy of bubbling solutions

We present a comprehensive analysis of holography for the bubbling solutions of Lin-Lunin-Maldacena. These solutions are uniquely determined by a coloring of a 2-plane, which was argued to correspond to the phase space of free fermions. We show that in general this phase space distribution does not determine fully the 1/2 BPS state of N=4 SYM that the gravitational solution is dual to, but it does determine it enough so that vevs of all single trace 1/2 BPS operators in that state are uniquely determined to leading order in the large N limit. These are precisely the vevs encoded in the asymptotics of the LLM solutions. We extract these vevs for operators up to dimension 4 using holographic renormalization and KK holography and show exact agreement with the field theory expressions.Comment: 67 pages, 6 figures; v2: typos corrected, refs added; v3: expanded explanations, more typos correcte

Statistical Mechanics of Three-dimensional Kerr-de Sitter Space

The statistical computation of the (2+1)-dimensional Kerr-de Sitter space in the context of the {\it classical} Virasoro algebra for an asymptotic isometry group has been a mystery since first, the degeneracy of the states has the right value only at the infinite boundary which is casually disconnected from our universe, second, the analyses were based on the unproven Cardy's formula for complex central charge and conformal weight. In this paper, I consider the entropy in Carlip's "would-be gauge" degrees of freedom approach instead. I find that it agree with the Bekenstein-Hawking entropy but there are no the above problems. Implications to the dS/CFT are noted.Comment: Added comments about diffeomorphism generators and Wheeler-de Witt equation; Added references; Accpected in CQ

Mergers and Typical Black Hole Microstates

We use mergers of microstates to obtain the first smooth horizonless microstate solutions corresponding to a BPS three-charge black hole with a classically large horizon area. These microstates have very long throats, that become infinite in the classical limit; nevertheless, their curvature is everywhere small. Having a classically-infinite throat makes these microstates very similar to the typical microstates of this black hole. A rough CFT analysis confirms this intuition, and indicates a possible class of dual CFT microstates. We also analyze the properties and the merging of microstates corresponding to zero-entropy BPS black holes and black rings. We find that these solutions have the same size as the horizon size of their classical counterparts, and we examine the changes of internal structure of these microstates during mergers.Comment: 49 pages, 5 figures. v2 references adde