Superconformal Field Theory with Boundary: Fermionic Model

Fermionic model of Superconformal field theory with boundary is considered. There were written the ''boundary'' Ward Identity for this theory and also constructed boundary states for fermionic and spin models. For this model were derived ''bootstrap'' equations for boundary structure constants.Comment: 12 page

The Trace Problem for Toeplitz Matrices and Operators and its Impact in Probability

The trace approximation problem for Toeplitz matrices and its applications to stationary processes dates back to the classic book by Grenander and Szeg\"o, "Toeplitz forms and their applications". It has then been extensively studied in the literature. In this paper we provide a survey and unified treatment of the trace approximation problem both for Toeplitz matrices and for operators and describe applications to discrete- and continuous-time stationary processes. The trace approximation problem serves indeed as a tool to study many probabilistic and statistical topics for stationary models. These include central and non-central limit theorems and large deviations of Toeplitz type random quadratic functionals, parametric and nonparametric estimation, prediction of the future value based on the observed past of the process, etc. We review and summarize the known results concerning the trace approximation problem, prove some new results, and provide a number of applications to discrete- and continuous-time stationary time series models with various types of memory structures, such as long memory, anti-persistent and short memory

Comparing 3C 120 jet emission at small and large scales

Context. Important information on the evolution of the jet can be obtained by comparing the physical state of the plasma at its propagation through the broad-line region (where the jet is most likely formed) into the intergalactic medium, where it starts to significantly decelerate. Aims. We compare the constraints on the physical parameters in the innermost ($\leq$ pc) and outer ($\geq$ kpc) regions of the 3C 120 jet by means of a detailed multiwavelength analysis and theoretical modeling of their broadband spectra. Methods.The data collected by Fermi LAT, Swift and Chandra are analyzed together and the spectral energy distributions are modeled using a leptonic synchrotron and inverse Compton model, taking into account the seed photons originating inside and outside of the jet. The model parameters are estimated using the MCMC method. Results. The $\gamma$-ray flux from the inner jet of 3C 120 was characterized by rapid variation from MJD 56900 to MJD 57300. Two strong flares were observed on April 24, 2015 when, within 19.0 minutes and 3.15 hours the flux was as high as $(7.46\pm1.56)\times10^{-6}photon\:cm^{-2}\:s^{-1}$ and $(4.71\pm0.92)\times10^{-6}photon\:cm^{-2}\:s^{-1}$ respectively. The broadband emission in the quiet and flaring states can be described as SSC emission while IC scattering of dusty torus photons cannot be excluded for the flaring states. The X-ray emission from the knots can be well reproduced by IC scattering of CMB photons only if the jet is highly relativistic (since even when $\delta=10$ still $U_{\rm e}/U_B\geq80$). These extreme requirements can be somewhat softened assuming the X-rays are from the synchrotron emission of a second population of very-high-energy electrons. Conclusions. We found that the jet power estimated at two scales is consistent, suggesting that the jet does not suffer severe dissipation, it simply becomes radiatively inefficient.Comment: Accepted for publication in Astronomy & Astrophysics. The abstract has been shortened to comply with the size limit set by arXi