Color superconductivity, BPS strings and monopole confinement in N=2 and N=4 super Yang-Mills theories

We review some recent developments on BPS string solutions and monopole confinement in the Higgs or (color) superconducting phase of deformed N=2 and N=4 super Yang-Mills theories. In particular, the monopole magnetic fluxes are shown to be always integer linear combinations of string fluxes. Moreover, a bound for the threshold length of the string breaking is obtained. When the gauge group SU(N) is broken to Z_N, the BPS string tension satisfies the Casimir scaling law. Furthermore in the SU(3) case the string solutions are such that they allow the formation of a confining system with three monopoles.Comment: 9 pages, 2 figures, invited talk given at 24th Brazilian National Meeting on Particles and Field

Generalised Abelian Chern-Simons Theories and their Connection to Conformal Field Theories

We discuss the generalization of Abelian Chern-Simons theories when $\theta$-angles and magnetic monopoles are included. We map sectors of two dimensional Conformal Field Theories into these three dimensional theories.Comment: 9 page

The Extended Fock Basis of Clifford Algebra

We investigate the properties of the Extended Fock Basis (EFB) of Clifford algebras introduced in [1]. We show that a Clifford algebra can be seen as a direct sum of multiple spinor subspaces that are characterized as being left eigenvectors of \Gamma. We also show that a simple spinor, expressed in Fock basis, can have a maximum number of non zero coordinates that equals the size of the maximal totally null plane (with the notable exception of vectorial spaces with 6 dimensions).Comment: Minimal corrections to the published versio

Products of multisymplectic manifolds and homotopy moment maps

Multisymplectic geometry admits an operation that has no counterpart in symplectic geometry, namely, taking the product of two multisymplectic manifolds endowed with the wedge product of the multisymplectic forms. We show that there is an L-infinity-embedding of the L-infinity-algebra of observables of the individual factors into the observables of the product, and that homotopy moment maps for the individual factors induce a homotopy moment map for the product. As a by-product, we associate to every multisymplectic form a curved L-infinity-algebra, whose curvature is the multisymplectic form itself.Comment: 27 pages. Version to be published in Journal of Lie Theor

A Theory of the IMF for Star Formation in Molecular Clouds

We present models for the initial mass function (IMF) for stars forming within molecular clouds. These models use the idea that stars determine their own masses through the action of powerful stellar outflows. This concept allows us to calculate a semi-empirical mass formula (SEMF), which provides the transformation between initial conditions in molecular clouds and the final masses of forming stars. For a particular SEMF, a given distribution of initial conditions predicts a corresponding IMF. We consider several different descriptions for the distribution of initial conditions in star forming molecular clouds. We first consider the limiting case in which only one physical variable -- the effective sound speed -- determines the initial conditions. In this limit, we use observed scaling laws to determine the distribution of sound speed and the SEMF to convert this distribution into an IMF. We next consider the opposite limit in which many different independent physical variables play a role in determining stellar masses. In this limit, the central limit theorem shows that the IMF approaches a log-normal form. Realistic star forming regions contain an intermediate number of relevant variables; we thus consider intermediate cases between the two limits. Our results show that this picture of star formation and the IMF naturally produces stellar mass distributions that are roughly consistent with observations. This paper thus provides a calculational framework to construct theoretical models of the IMF.Comment: 34 pages, 7 figures available on reques

Ant routing algorithm for the Lightning Network

We propose a decentralized routing algorithm that can be implemented in Bitcoin Lightning Network. All nodes in the network contribute equally to path searching. The algorithm is inspired from ant path searching algorithms.Comment: 10 pages, 1 figur

Learning by Suing: Structural Estimates of Court Errors in Patent Litigation

This paper presents structural estimates of the probability of validity, and the probability of Type I and Type II errors by courts in patent litigation. Patents are modeled as uncertain property rights, and implications of the model are tested using stock market reactions to patent litigation decisions. The estimation quantifies beliefs about patent validity and court errors in a Bayesian context. I estimate that the underlying beliefs about validity range from 0.6 to 0.7 for litigated patents. Market beliefs about courts show that Type I errors (finding a valid patent invalid) occur very frequently–an estimated probability of 0.45. However, Type II errors (finding an invalid patent valid) occur with near zero probability. Additional implications of the model address patent value. My results are the first structural estimates of court errors. Additionally, this study is the first to perform event studies on patent litigation.

Effects of Turbulence on Cosmic Ray Propagation in Protostars and Young Star/Disk Systems

The magnetic fields associated with young stellar objects are expected to have an hour-glass geometry, i.e., the magnetic field lines are pinched as they thread the equatorial plane surrounding the forming star but merge smoothly onto a background field at large distances. With this field configuration, incoming cosmic rays experience both a funneling effect that acts to enhance the flux impinging on the circumstellar disk and a magnetic mirroring effect that acts to reduce that flux. To leading order, these effects nearly cancel out for simple underlying magnetic field structures. However, the environments surrounding young stellar objects are expected to be highly turbulent. This paper shows how the presence of magnetic field fluctuations affects the process of magnetic mirroring, and thereby changes the flux of cosmic rays striking circumstellar disks. Turbulence has two principle effects: 1) The (single) location of the magnetic mirror point found in the absence of turbulence is replaced with a wide distribution of values. 2) The median of the mirror point distribution moves outward for sufficiently large fluctuation amplitudes (roughly when $\delta B/B_0>0.2$ at the location of the turbulence-free mirror point); the distribution becomes significantly non-gaussian in this regime as well. These results may have significant consequences for the ionization fraction of the disk, which in turn dictates the efficiency with which disk material can accrete onto the central object. A similar reduction in cosmic ray flux can occur during the earlier protostellar stages; the decrease in ionization can help alleviate the magnetic braking problem that inhibits disk formation.Comment: Accepted for publication in The Astrophysical Journa

The dynamics of patent citations

The use of patent citations as a measure of patent "quality" increased dramatically in recent years. I estimate the hazard of patent citation, and find evidence of unobserved heterogeneity. Hazard estimation provides a means to separate patent quality from citation "inflation."