Contact Term, its Holographic Description in QCD and Dark Energy

In this work we study the well known contact term, which is the key element in resolving the so-called $U(1)_A$ problem in QCD. We study this term using the dual Holographic Description. We argue that in the dual picture the contact term is saturated by the D2 branes which can be interpreted as the tunnelling events in Minkowski space-time. We quote a number of direct lattice results supporting this identification. We also argue that the contact term receives a Casimir -like correction \sim (\Lqcd R)^{-1} rather than naively expected \exp(-\Lqcd R) when the Minkowski space-time ${\cal R}_{3,1}$ is replaced by a large but finite manifold with a size $R$. Such a behaviour is consistent with other QFT-based computations when power like corrections are due to nontrivial properties of topological sectors of the theory. In holographic description such a behaviour is due to massless Ramond-Ramond (RR) field living in the bulk of multidimensional space when power like corrections is a natural outcome of massless RR field. In many respects the phenomenon is similar to the Aharonov -Casher effect when the "modular electric field" can penetrate into a superconductor where the electric field is exponentially screened. The role of "modular operator" from Aharonov -Casher effect is played by large gauge transformation operator $\cal{T}$ in 4d QCD, resulting the transparency of the system to topologically nontrivial pure gauge configurations. We discuss some profound consequences of our findings. In particular, we speculate that a slow variation of the contact term in expanding universe might be the main source of the observed Dark Energy.Comment: Final version to appear in Phys. Rev. D. Comments added on interpretation of the "topological Casimir effect" from 5d viewpoint where it can be thought as conventional Casimir effec

Are You Ready for Some Football?: How Antitrust Laws Can Be Used to Break Up DirecTV\u27s Exclusive Right to Telecast NFL\u27s Sunday Ticket Package

There is almost no question that football has become modem America\u27s pastime. Football has never been more popular, and every Sunday people are clamoring to watch as many games as possible. The Sunday Ticket package allows viewers to watch any National Football League ( NFL ) game being played at any given time. However, the NFL has only granted DirecTV the right to air the Sunday Ticket package, denying this excellent service to a majority of television viewers. By limiting the reach of the Sunday Ticket package, the NFL may be in violation of antitrust laws. This Note begins by explaining antitrust laws, and then moves on to discussing the history of professional football and its complicated relationship with television. Finally, the Note argues that several aspects of NFL\u27s agreement with DirecTV violate antitrust laws, and that making the Sunday Ticket package more widely available would benefit consumers

Are You Ready for Some Football?: How Antitrust Laws Can Be Used to Break Up DirecTV\u27s Exclusive Right to Telecast NFL\u27s Sunday Ticket Package

There is almost no question that football has become modem America\u27s pastime. Football has never been more popular, and every Sunday people are clamoring to watch as many games as possible. The Sunday Ticket package allows viewers to watch any National Football League ( NFL ) game being played at any given time. However, the NFL has only granted DirecTV the right to air the Sunday Ticket package, denying this excellent service to a majority of television viewers. By limiting the reach of the Sunday Ticket package, the NFL may be in violation of antitrust laws. This Note begins by explaining antitrust laws, and then moves on to discussing the history of professional football and its complicated relationship with television. Finally, the Note argues that several aspects of NFL\u27s agreement with DirecTV violate antitrust laws, and that making the Sunday Ticket package more widely available would benefit consumers

Tentative detection of the gravitational magnification of type Ia supernovae

The flux from distant type Ia supernovae (SN) is likely to be amplified or de-amplified by gravitational lensing due to matter distributions along the line-of-sight. A gravitationally lensed SN would appear brighter or fainter than the average SN at a particular redshift. We estimate the magnification of 26 SNe in the GOODS fields and search for a correlation with the residual magnitudes of the SNe. The residual magnitude, i.e. the difference between observed and average magnitude predicted by the "concordance model" of the Universe, indicates the deviation in flux from the average SN. The linear correlation coefficient for this sample is r=0.29. For a similar, but uncorrelated sample, the probability of obtaining a correlation coefficient equal to or higher than this value is ~10%, i.e. a tentative detection of lensing at ~90% confidence level. Although the evidence for a correlation is weak, our result is in accordance with what could be expected given the small size of the sample.Comment: 7 pages, 2 figure

Casimir forces in Bose-Einstein condensates: finite size effects in three-dimensional rectangular cavities

The Casimir force due to {\it thermal} fluctuations (or pseudo-Casimir force) was previously calculated for the perfect Bose gas in the slab geometry for various boundary conditions. The Casimir pressure due to {\it quantum} fluctuations in a weakly-interacting dilute Bose-Einstein condensate (BEC) confined to a parallel plate geometry was recently calculated for Dirichlet boundary conditions. In this paper we calculate the Casimir energy and pressure due to quantum fluctuations in a zero-temperature homogeneous weakly-interacting dilute BEC confined to a parallel plate geometry with periodic boundary conditions and include higher-order corrections which we refer to as Bogoliubov corrections. The leading order term is identified as the Casimir energy of a massless scalar field moving with wave velocity equal to the speed of sound in the BEC. We then obtain the leading order Casimir pressure in a general three-dimensional rectangular cavity of arbitrary lengths and obtain the finite-size correction to the parallel plate scenario.Comment: 12 pages; no figures; v.2: version accepted for publication in JSTAT v.3: references adde

Diffusion Limited Aggregation on a Cylinder

We consider the DLA process on a cylinder G x N. It is shown that this process "grows arms", provided that the base graph G has small enough mixing time. Specifically, if the mixing time of G is at most (log|G|)^(2-\eps), the time it takes the cluster to reach the m-th layer of the cylinder is at most of order m |G|/loglog|G|. In particular we get examples of infinite Cayley graphs of degree 5, for which the DLA cluster on these graphs has arbitrarily small density. In addition, we provide an upper bound on the rate at which the "arms" grow. This bound is valid for a large class of base graphs G, including discrete tori of dimension at least 3. It is also shown that for any base graph G, the density of the DLA process on a G-cylinder is related to the rate at which the arms of the cluster grow. This implies, that for any vertex transitive G, the density of DLA on a G-cylinder is bounded by 2/3.Comment: 1 figur

Collective decision-making on triadic graphs

Many real-world networks exhibit community structures and non-trivial clustering associated with the occurrence of a considerable number of triangular subgraphs known as triadic motifs. Triads are a set of distinct triangles that do not share an edge with any other triangle in the network. Network motifs are subgraphs that occur significantly more often compared to random topologies. Two prominent examples, the feedforward loop and the feedback loop, occur in various real-world networks such as gene-regulatory networks, food webs or neuronal networks. However, as triangular connections are also prevalent in communication topologies of complex collective systems, it is worthwhile investigating the influence of triadic motifs on the collective decision-making dynamics. To this end, we generate networks called Triadic Graphs (TGs) exclusively from distinct triadic motifs. We then apply TGs as underlying topologies of systems with collective dynamics inspired from locust marching bands. We demonstrate that the motif type constituting the networks can have a paramount influence on group decision-making that cannot be explained solely in terms of the degree distribution. We find that, in contrast to the feedback loop, when the feedforward loop is the dominant subgraph, the resulting network is hierarchical and inhibits coherent behavior

The localization transition at finite temperatures: electric and thermal transport

The Anderson localization transition is considered at finite temperatures. This includes the electrical conductivity as well as the electronic thermal conductivity and the thermoelectric coefficients. An interesting critical behavior of the latter is found. A method for characterizing the conductivity critical exponent, an important signature of the transition, using the conductivity and thermopower measurements, is outlined.Comment: Article for the book: "50 Years of Anderson Localization", edited by E. Abrahams (World Scientific, Singapore, 2010