On NMHV form factors in N=4 SYM theory from generalized unitarity

In this paper a supersymmetric version of a generalized unitarity cut method in application to MHV and NMHV for form factors of operators from the N=4 SYM stress-tensor current supermultiplet $T^{AB}$ at one loop is discussed. The explicit answers for 3 and 4 point NMHV form factors at tree and one loop level are obtained. The general structure of n-point NMHV form factor at one loop is discussed as well as the relation between form factor with super momentum equal to zero and the logarithmic derivative of the superamplitude with respect to the coupling constant.Comment: Latex, 43 pages, 11 figures; v3: JHEP ver., minor changes, typos corrected, ref. adde

Training computer personnel : the problem and possible solution

This document addresses a very serious problem; our present methods of training computer specialists, of all types and levels are inadequate for the task. We are producing too few experts and projections indicate an ever greater gap between supply and demand. This shortage affects computer scientists from B. S. to Ph.D. as well as other computer personnel. ..

Four dimensional ambitwistor strings and form factors of local and Wilson line operators

We consider the description of form factors of local and Wilson line operators (reggeon amplitudes) in N=4 SYM within the framework of four dimensional ambitwistor string theory. We present the explicit expressions for string composite operators corresponding to stress-tensor operator supermultiplet and Wilson line operator insertion. It is shown, that corresponding tree-level string correlation functions correctly reproduce previously obtained Grassmannian integral representations. As by product we derive four dimensional tree-level scattering equations representations for the mentioned form factors and formulate a simple gluing procedure used to relate operator form factors with on-shell amplitudes.Comment: 46 pages, 3 figures; v3: multiple changes in the text, typos corrected, references adde

Ambitwistor strings and reggeon amplitudes in N=4 SYM

We consider the description of reggeon amplitudes (Wilson lines form factors) in N=4 SYM within the framework of four dimensional ambitwistor string theory. The latter is used to derive scattering equations representation for reggeon amplitudes with multiple reggeized gluons present. It is shown, that corresponding tree-level string correlation function correctly reproduces previously obtained Grassmannian integral representation of reggeon amplitudes in N=4 SYM.Comment: 18 page

Grassmannian Integral for General Gauge Invariant Off-shell Amplitudes in N=4 SYM

In this paper we consider tree-level gauge invariant off-shell amplitudes (Wilson line form factors) in $\mathcal{N}=4$ SYM with arbitrary number of off-shell gluons or equivalently Wilson line operator insertions. We make a conjecture for the Grassmannian integral representation for such objects and verify our conjecture on several examples. It is remarkable that in our formulation one can consider situation when on-shell particles are not present at all, i.e. we have Grassmannian integral representation for purely off-shell object. In addition we show that off-shell amplitude with arbitrary number of off-shell gluons could be also obtained using quantum inverse scattering method for auxiliary $\mathfrak{gl}(4|4)$ super spin chain.Comment: 38 pages, 9 figures; v4: typos corrected, comment in section 3.2 adde

Phase-tunable Majorana bound states in a topological N-SNS junction

We theoretically study the differential conductance of a one-dimensional normal-superconductor-normal-superconductor (N-SNS) junction with a phase bias applied between the two superconductors. We consider specifically a junction formed by a spin-orbit coupled semiconducting nanowire with regions of the nanowire having superconducting pairing induced by a bulk $s$-wave superconductor. When the nanowire is tuned into a topologically non-trivial phase by a Zeeman field, it hosts zero-energy Majorana modes at its ends as well as at the interface between the two superconductors. The phase-dependent splitting of the Majorana modes gives rise to features in the differential conductance that offer a clear distinction between the topologically trivial and non-trivial phases. We calculate the transport properties of the junction numerically and also present a simple analytical model that captures the main properties of the predicted tunneling spectroscopy.Comment: 11 pages, 7 figure

Identification of Macroeconomic Factors in Large Panels

This paper presents a dynamic factor model where the extracted factors and shocks are given a clear economic interpretation. The economic interpretation of the factors is obtained by means of a set of over-identifying loading restrictions, while the structural shocks are estimated following standard practices in the SVAR literature. Estimators based on the EM algorithm are developed. We apply this framework to a large panel of US monthly macroeconomic series. In particular, we identify five macroeconomic factors and discuss the economic impact of monetary policy shocks. The results are theoretically more plausible than those implied by standard SVAR models and indicate a significant role for monetary policy shocks in macroeconomic dynamics.Monetary policy, Business Cycles, Factor Models, EM Algorithm.