A Supersymmetry Preserving Mass-Deformation of N=1 Super Yang-Mills in D=2+1

We construct a massive non-abelian N= 1 SYM theory on R^3. This is achieved by using a non-local gauge and Poincare invariant mass term for gluons due to Nair. The underlying supersymmetry algebra is shown to be a non-central extension of the Poincare algebra by the spacetime rotation group so(3). The incorporation of Chern-Simons couplings in the formalism is also presented. The dimensional reduction of the gauge theory and the SUSY algebra is related to a massive N=2 massive matrix quantum mechanics based on euclidean $Clifford_2(R)$

Inseparability inequalities for higher-order moments for bipartite systems

There are several examples of bipartite entangled states of continuous variables for which the existing criteria for entanglement using the inequalities involving the second order moments are insufficient. We derive new inequalities involving higher order correlation, for testing entanglement in non-Gaussian states. In this context we study an example of a non-Gaussian state, which is a bipartite entangled state of the form $\psi(x_{\rm a},x_{\rm b})\propto (\alpha x_{\rm a}+\beta x_{\rm b})e^{-(x_{\rm a}^2+x_{\rm b}^2)/2}$. Our results open up an avenue to search for new inequalities to test entanglement in non-Gaussian states.Comment: 7 pages, Submitte

The Cosmic Mach Number: Comparison from Observations, Numerical Simulations and Nonlinear Predictions

We calculate the cosmic Mach number M - the ratio of the bulk flow of the velocity field on scale R to the velocity dispersion within regions of scale R. M is effectively a measure of the ratio of large-scale to small-scale power and can be a useful tool to constrain the cosmological parameter space. Using a compilation of existing peculiar velocity surveys, we calculate M and compare it to that estimated from mock catalogues extracted from the LasDamas (a LCDM cosmology) numerical simulations. We find agreement with expectations for the LasDamas cosmology at ~ 1.5 sigma CL. We also show that our Mach estimates for the mocks are not biased by selection function effects. To achieve this, we extract dense and nearly-isotropic distributions using Gaussian selection functions with the same width as the characteristic depth of the real surveys, and show that the Mach numbers estimated from the mocks are very similar to the values based on Gaussian profiles of the corresponding widths. We discuss the importance of the survey window functions in estimating their effective depths. We investigate the nonlinear matter power spectrum interpolator PkANN as an alternative to numerical simulations, in the study of Mach number.Comment: 12 pages, 9 figures, 3 table

Aspects of Integrability in N =4 SYM

Various recently developed connections between supersymmetric Yang-Mills theories in four dimensions and two dimensional integrable systems serve as crucial ingredients in improving our understanding of the AdS/CFT correspondence. In this review, we highlight some connections between superconformal four dimensional Yang-Mills theory and various integrable systems. In particular, we focus on the role of Yangian symmetries in studying the gauge theory dual of closed string excitations. We also briefly review how the gauge theory connects to Calogero models and open quantum spin chains through the study of the gauge theory duals of D3 branes and open strings ending on them. This invited review, written for Modern Physics Letters-A, is based on a seminar given at the Institute of Advanced Study, Princeton.Comment: Invited brief review for Mod. Phys. Lett. A based on a talk at I.A.S, Princeto