Harmonic Potential and BMN energies

Investigation of analytical and numerical solutions for one-dimensional independent-oftime Schrödinger Equation

In this paper, the numerical solution methods of one- particale, one – dimensional time- independentSchrodinger equation are presented that allows one to obtain accurate bound state eigen values andeigen functions for an arbitrary potential energy function V(x). These methods included the FEM(Finite Element Method), Cooly, Numerov and others. Here we considered the Numerov method inmore details...

Correlation Functions of Complex Matrix Models

For a restricted class of potentials (harmonic+Gaussian potentials), we express the resolvent integral for the correlation functions of simple traces of powers of complex matrices of size N , in term of a determinant; this determinant is function of four kernels constructed from the orthogonal polynomials corresponding to the potential and from their Cauchy transform. The correlation functions ...

All loop BMN state energies from matrices

We study a quantum corrected SO(6) invariant matrix quantum mechanics obtained from the s-wave modes of the scalars of N = 4 SYM on S. For commuting matrices, this model is believed to describe the 1/8 BPS states of the full SYM theory. In the large N limit the ground state corresponds to a distribution of eigenvalues on a S which we identify with the sphere on the dual geometry AdS5×S. We then...

Potential Harmonic Calculations of theBinding Energies of

On Half-BPS States of the ABJM Theory

We analyze SU(2) invariant half-BPS states of the 3d, N = 8 or N = 6 SCFT within the radial quantization of the ABJM theory [1], the theory proposed to describe N M2-branes in the R × C/Zk background. After studying the classical moduli space of these configurations, we explicitly construct a set of gauge invariant operators involving ’t Hooft monopole operators corresponding to these states. W...