Black Hole Statistics from Holography

We study the microstates of the ``small'' black hole in the \half-BPS sector of AdS$_5\times S^5$, the superstar of Myers and Tafjord, using the powerful holographic description provided by LLM. The system demonstrates the inherently statistical nature of black holes, with the geometry of Myer and Tafjord emerging only after averaging over an ensemble of geometries. The individual microstate geometries differ in the highly non-trivial topology of a quantum foam at their core, and the entropy can be understood as a partition of $N$ units of flux among 5-cycles, as required by flux quantization. While the system offers confirmation of the most controversial aspect of Mathur and Lunin's recent ``fuzzball'' proposal, we see signs of a discrepancy in interpreting its details.Comment: 21 pages, 4 figures; References adde

Complex Matrix Model and Fermion Phase Space for Bubbling AdS Geometries

We study a relation between droplet configurations in the bubbling AdS geometries and a complex matrix model that describes the dynamics of a class of chiral primary operators in dual N=4 super Yang Mills (SYM). We show rigorously that a singlet holomorphic sector of the complex matrix model is equivalent to a holomorphic part of two-dimensional free fermions, and establish an exact correspondence between the singlet holomorphic sector of the complex matrix model and one-dimensional free fermions. Based on this correspondence, we find a relation of the singlet holomorphic operators of the complex matrix model to the Wigner phase space distribution. By using this relation and the AdS/CFT duality, we give a further evidence that the droplets in the bubbling AdS geometries are identified with those in the phase space of the one-dimensional fermions. We also show that the above correspondence actually maps the operators of N=4 SYM corresponding to the (dual) giant gravitons to the droplet configurations proposed in the literature.Comment: 27 pages, 6 figures, some clarification, typos corrected, published versio

Rational foundation of GR in terms of statistical mechanic in the AdS/CFT framework

In this article, we work out the microscopic statistical foundation of the supergravity description of the simplest 1/2 BPS sector in the AdS(5)/CFT(4). Then, all the corresponding supergravity observables are related to thermodynamical observables, and General Relativity is understood as a mean-field theory. In particular, and as an example, the Superstar is studied and its thermodynamical properties clarified.Comment: 13 pages, 6 eps figures, latex, some improvements introduced, reference added, typos correcte

Effect of Finite Granularity of Detectors on Anisotropy Coefficients

The coefficients that describe the anisotropy in the azimuthal distribution of particles are lower when the particles are recorded in a detector with finite granularity and measures only hits. This arises due to loss of information because of multiple hits in any channel. The magnitude of this loss of signal depends both on the occupancy and on the value of the coefficient. These correction factors are obtained for analysis methods differing in detail, and are found to be different.Comment: 11 pages including 2 figure

Semi-classical Probe Strings on Giant Gravitons Backgrounds

In the first part of this paper we study two $Z_2$ symmetries of the LLM metric, both of which exchange black and white regions. One of them which can be interpreted as the particle-hole symmetry is the symmetry of the whole supergravity solution while the second one is just the symmetry of the metric and changes the sign of the fivefrom flux. In the second part of the paper we use closed string probes and their semi-classical analysis to compare the two 1/2 BPS deformations of $AdS_5\times S^5$, the smooth LLM geometry which contains localized giant gravitons and the superstar case which is a solution with naked singularity corresponding to smeared giants. We discuss the realization of the $Z_2$ symmetry in the semi-classical closed string probes point of view.Comment: 29 pages, 6 .eps figures; v2: References adde

Bosonization of non-relativstic fermions in 2-dimensions and collective field theory

We revisit bosonization of non-relativistic fermions in one space dimension. Our motivation is the recent work on bubbling half-BPS geometries by Lin, Lunin and Maldacena (hep-th/0409174). After reviewing earlier work on exact bosonization in terms of a noncommutative theory, we derive an action for the collective field which lives on the droplet boundaries in the classical limit. Our action is manifestly invariant under time-dependent reparametrizations of the boundary. We show that, in an appropriate gauge, the classical collective field equations imply that each point on the boundary satisfies Hamilton's equations for a classical particle in the appropriate potential. For the harmonic oscillator potential, a straightforward quantization of this action can be carried out exactly for any boundary profile. For a finite number of fermions, the quantum collective field theory does not reproduce the results of the exact noncommutative bosonization, while the latter are in complete agreement with the results computed directly in the fermi theory.Comment: references added and typos corrected; 21 pages, 3 figures, eps

The M2/M5 BPS Partition Functions from Supergravity

In the framework of the AdS/CFT duality, we calculate the supersymmetric partition function of the superconformal field theories living in the world volume of either $N$ $M2$-branes or $N$ $M5$-branes. We used the dual supergravity partition function in a saddle point approximation over supersymmetric Black Holes. Since our BHs are written in asymptotically global $AdS_{d+1}$ co-ordinates, the dual SCFTs are in $R x S^{d}$ for $d=2,5$. The resulting partition function shows phase transitions, constraints on the phase space and allowed us to identify unstable BPS Black hole in the $AdS$ phase. These configurations should correspond to unstable configurations in the dual theory. We also report an intriguing relation between the most general Witten Index, computed in the above theories, and our BPS partition functions.Comment: 9 pages, 2 columns, 4 figures, revtex, typos corrected, reference adde

Delivery time dynamics in an assemble-to-order inventory and order based production control system

System dynamics play a critical role in influencing supply chain performance. However, the dynamic property of the assemble-to-order (ATO) system remain unexplored. Based on control theory, the inventory and order based production control system (IOBPCS) family, can be utilized as a base framework for assessing system dynamics. However, the underlying assumption in traditional IOBPCS-based analytical studies is that the system is linear and the delivery time to end customers is negligible or backlog is used as a surrogate indicator. Our aim is to incorporate customer delivery lead-time variance as the third assessment measure alongside capacity availability and inventory variance as part of the so-called ‘performance triangle’– capacity at the supplier, the customer order decoupling point (CODP) inventory and the delivery lead-time. Using the ‘performance triangle’ and adopting non-linear control engineering techniques, we assess the dynamic behaviour of an ATO system in the electronics sector. We benchmark the ATO system dynamics model against the IOBPCS family. We exploit frequency response analysis to ensure a robust system design by considering three measures of the ‘performance triangle’. The findings suggest delivery LT variance can be minimised by maintaining the ATO system as a true Push-Pull hybrid state with sufficient CODP stock, although increased operational cost driven by bullwhip and CODP variance need to be considered. However, if the hybrid ATO system 'switches' to the pure Push state, the mean and variance of delivery LT can be significantly increased

Modeliranje, upravljanje i eksperimentalno istraživanje novoga raspodijeljenog statičkog kompenzatora jalove snage zasnovanog na višestupanjskom pretvaraču s ulančenim H-mostovima

A novel static synchronous compensator for reactive power compensation of distribution system (DSTATCOM) is proposed, based on the cascaded H-bridge multilevel inverter configuration. The mathematical formulation of the multilevel DSTATCOM is presented using state-space representations. A new software phase-locked loop (SPLL) is presented for grid synchronization and the obtained phase angle of the fundamental component of the grid voltage is utilized for deriving the active and reactive power balancing equations of the multilevel DSTATCOM. The proportional-resonant (PR) controller scheme is adopted for the current tracking control of the inverter, and the average dc-link voltage is controlled using a proportional-integral (PI) controller to regulate the active power flow of the DSTATCOM. Besides, the voltage balancing (VB) control among individual H-bridges is achieved by using separate PI regulators to control the difference voltage between the individual dc-link voltage and the average dc-link voltage. The validity of the proposed multilevel DSTATCOM and its control strategies is substantially confirmed by the extensive simulation results and the experimental results from the prototype system.Predložen je novi statički sinkroni kompenzator za kompenzaciju jalove snage distribucijskog sustava (DSTATCOM) zasnovan na konfiguraciji višestupanjskog pretvarača s ulančenim H-mostovima. Matematički model višerazinskog DSTATCOM-a prikazan je u prostoru stanja. Predstavljena je nova programski izvedena petlja sa zaključanom fazom namijenjena sinkronizaciji s mrežom, a dobiveni fazni kut osnovne komponente mrežnog napona koristi se za izvod jednadžbi ravnoteže aktivne i jalove snage višerazinskog DSTATCOM-a. Usvojen je koncept proporcionalno-rezonantnog regulatora za slijeđenje trajektorije struje pretvarača, a srednji napon istosmjernog međukruga upravlja se korištenjem proporcionalno-integracijskog (PI) regulatora u svrhu regulacije toka radne snage DSTATCOM-a. Osim toga, upravljanje uravnoteženjem napona među pojedinim H-mostovima ostvareno je korištenjem odvojenih PI regulatora za upravljanje razlikom napona među pojedinim istosmjernim međukrugovima te srednjim naponom istosmjernih međukrugova. Valjanost predloženog višestupanjskog DSTATCOM-a i primijenjenih upravljačkih strategija potvrđena je brojnim simulacijskim i eksperimentalnim rezultatima na prototipskoj izvedbi ovog sustava

Extended Fermion Representation of Multi-Charge 1/2-BPS Operators in AdS/CFT -- Towards Field Theory of D-Branes --

We extend the fermion representation of single-charge 1/2-BPS operators in the four-dimensional N=4 super Yang-Mills theory to general (multi-charge) 1/2-BPS operators such that all six directions of scalar fields play roles on an equal footing. This enables us to construct a field-theorectic representation for a second-quantized system of spherical D3-branes in the 1/2-BPS sector. The Fock space of D3-branes is characterized by a novel exclusion principle (called `Dexclusion' principle), and also by a nonlocality which is consistent with the spacetime uncertainty relation. The Dexclusion principle is realized by composites of two operators, obeying the usual canonical anticommutation relation and the Cuntz algebra, respectively. The nonlocality appears as a consequence of a superselction rule associated with a symmetry which is related to the scale invariance of the super Yang-Mills theory. The entropy of the so-called superstars, with multiple charges, which have been proposed to be geometries corresponding to the condensation of giant gravitons is discussed from our viewpoint and is argued to be consistent with the Dexclusion principle. Our construction may be regarded as a first step towards a possible new framework of general D-brane field theory.Comment: 43 pages, 4 figures; version 2, corrected typos and added reference