On Coordinate Independent State Space of Matrix Theory

Abstract

We investigate symmetry structure of coordinate independent states in Matrix theory. Those states are building blocks of gauge invariant wavefunctions, and especially we consider zero energy bound state wavefunctions. First we construct some states in lower representations of the space rotation group SO(9) explicitly in the case of SU(2) gauge group, and classify them into SU(2) representations. Next we count the multiplicities of SO(9)×SU(N ) representations in the coordinate independent state space by using the notion of characters in group theory. For N = 2 case we give complete decomposition of the space into SO(9)×SU(2) representations, and give partial results for higher gauge groups.at East Tennessee State University on June 21, 2015

Superconformal Yang-Mills quantum mechanics and Calogero model with $$ {\text{OSp}}\left( {\mathcal{N}|{2},\mathbb{R}} \right) $$ symmetry

“…Further, in the large K limit or the planar limit, up to the renormalization of the overall factor, it converges to the inverse of the Dedekind eta function (which is a common special function in the computation of string theory partition functions). For the path integral derivation of the formula (6.1) see [53] and for the case of N = 2 we refer to [54,55]. For generic N it is an open problem.…”