Mesonic Chiral Rings in Calabi-Yau Cones from Field Theory

We study the half-BPS mesonic chiral ring of the N=1 superconformal quiver theories arising from N D3-branes stacked at Y^pq and L^abc Calabi-Yau conical singularities. We map each gauge invariant operator represented on the quiver as an irreducible loop adjoint at some node, to an invariant monomial, modulo relations, in the gauged linear sigma model describing the corresponding bulk geometry. This map enables us to write a partition function at finite N over mesonic half-BPS states. It agrees with the bulk gravity interpretation of chiral ring states as cohomologically trivial giant gravitons. The quiver theories for L^aba, which have singular base geometries, contain extra operators not counted by the naive bulk partition function. These extra operators have a natural interpretation in terms of twisted states localized at the orbifold-like singularities in the bulk.Comment: Latex, 25pgs, 12 figs, v2: minor clarification

Transformation seismology: composite soil lenses for steering surface elastic Rayleigh waves.

Metamaterials are artificially structured media that exibit properties beyond those usually encountered in nature. Typically they are developed for electromagnetic waves at millimetric down to nanometric scales, or for acoustics, at centimeter scales. By applying ideas from transformation optics we can steer Rayleigh-surface waves that are solutions of the vector Navier equations of elastodynamics. As a paradigm of the conformal geophysics that we are creating, we design a square arrangement of Luneburg lenses to reroute Rayleigh waves around a building with the dual aim of protection and minimizing the effect on the wavefront (cloaking). To show that this is practically realisable we deliberately choose to use material parameters readily available and this metalens consists of a composite soil structured with buried pillars made of softer material. The regular lattice of inclusions is homogenized to give an effective material with a radially varying velocity profile and hence varying the refractive index of the lens. We develop the theory and then use full 3D numerical simulations to conclusively demonstrate, at frequencies of seismological relevance 3–10 Hz, and for low-speed sedimentary soil (v(s): 300–500 m/s), that the vibration of a structure is reduced by up to 6 dB at its resonance frequency

Quarks in an External Electric Field in Finite Temperature Large N Gauge Theory

We use a ten dimensional dual string background to aspects of the physics large N four dimensional SU(N) gauge theory, where its fundamental quarks are charged under a background electric field. The theory is N=2 supersymmetric for vanishing temperature and electric field. At zero temperature, we observe that the electric field induces a phase transition associated with the dissociation of the mesons into their constituent quarks. This is an analogue of an insulator-metal transition, since the system goes from being an insulator with zero current (in the applied field) to a conductor with free charge carriers (the quarks). At finite temperature this phenomenon persists, with the dissociation transition become subsumed into the more familiar meson melting transition. Here, the dissociation phenomenon reduces the critical melting temperature.Comment: 20 pages, multiple figures. Corrected typo

Current Oscillations, Interacting Hall Discs and Boundary CFTs

In this paper, we discuss the behavior of conformal field theories interacting at a single point. The edge states of the quantum Hall effect (QHE) system give rise to a particular representation of a chiral Kac-Moody current algebra. We show that in the case of QHE systems interacting at one point we obtain a ``twisted'' representation of the current algebra. The condition for stationarity of currents is the same as the classical Kirchoff's law applied to the currents at the interaction point. We find that in the case of two discs touching at one point, since the currents are chiral, they are not stationary and one obtains current oscillations between the two discs. We determine the frequency of these oscillations in terms of an effective parameter characterizing the interaction. The chiral conformal field theories can be represented in terms of bosonic Lagrangians with a boundary interaction. We discuss how these one point interactions can be represented as boundary conditions on fields, and how the requirement of chirality leads to restrictions on the interactions described by these Lagrangians. By gauging these models we find that the theory is naturally coupled to a Chern-Simons gauge theory in 2+1 dimensions, and this coupling is completely determined by the requirement of anomaly cancellation.Comment: 32 pages, LateX. Uses amstex, amssymb. Typos corrected. To appear in Int. J. Mod. Phys.

Equivalent continuous and discrete realizations of Levy flights: Model of one-dimensional motion of inertial particle

The paper is devoted to the relationship between the continuous Markovian description of Levy flights developed previously and their equivalent representation in terms of discrete steps of a wandering particle, a certain generalization of continuous time random walks. Our consideration is confined to the one-dimensional model for continuous random motion of a particle with inertia. Its dynamics governed by stochastic self-acceleration is described as motion on the phase plane {x,v} comprising the position x and velocity v=dx/dt of the given particle. A notion of random walks inside a certain neighbourhood L of the line v=0 (the x-axis) and outside it is developed. It enables us to represent a continuous trajectory of particle motion on the plane {x,v} as a collection of the corresponding discrete steps. Each of these steps matches one complete fragment of the velocity fluctuations originating and terminating at the "boundary" of L. As demonstrated, the characteristic length of particle spatial displacement is mainly determined by velocity fluctuations with large amplitude, which endows the derived random walks along the x-axis with the characteristic properties of Levy flights. Using the developed classification of random trajectories a certain parameter-free core stochastic process is constructed. Its peculiarity is that all the characteristics of Levy flights similar to the exponent of the Levy scaling law are no more than the parameters of the corresponding transformation from the particle velocity v to the related variable of the core process. In this way the previously found validity of the continuous Markovian model for all the regimes of Levy flights is explained

Born-Infeld Theory and Stringy Causality

Fluctuations around a non-trivial solution of Born-Infeld theory have a limiting speed given not by the Einstein metric but the Boillat metric. The Boillat metric is S-duality invariant and conformal to the open string metric. It also governs the propagation of scalars and spinors in Born-Infeld theory. We discuss the potential clash between causality determined by the closed string and open string light cones and find that the latter never lie outside the former. Both cones touch along the principal null directions of the background Born-Infeld field. We consider black hole solutions in situations in which the distinction between bulk and brane is not sharp such as space filling branes and find that the location of the event horizon and the thermodynamic properties do not depend on whether one uses the closed or open string metric. Analogous statements hold in the more general context of non-linear electrodynamics or effective quantum-corrected metrics. We show how Born-Infeld action to second order might be obtained from higher-curvature gravity in Kaluza-Klein theory. Finally we point out some intriguing analogies with Einstein-Schr\"odinger theory.Comment: 31 pages, 4 figures, LaTex; Some comments and references adde

Bessel Process and Conformal Quantum Mechanics

Different aspects of the connection between the Bessel process and the conformal quantum mechanics (CQM) are discussed. The meaning of the possible generalizations of both models is investigated with respect to the other model, including self adjoint extension of the CQM. Some other generalizations such as the Bessel process in the wide sense and radial Ornstein- Uhlenbeck process are discussed with respect to the underlying conformal group structure.Comment: 28 Page