Large N Structure of the IIB Matrix Model

Abstract

We study large N behavior of the IIB matrix model using the equivalence between the IIB matrix model for finite N and a field theory on a non-commutative periodic lattice with N x N sites. We find that the large N dependences of correlation functions can be obtained by naively counting the number of fields in the field theory on the non-commutative periodic lattice. Furthermore the large N scaling behavior of the coupling constant g is determined if we impose that the expectation values of Wilson loops are calculable.Comment: 10 pages, LaTeX, To be appeared in Prog. Theor. Phys. 105, (2001

Large N behaviors of the IIB matrix model and the regularized Schild models

“…However, we pointed out a possibility that the large-N behavior of the IIB matrix model and that of the supersymmetric Schild model with the momentum cut-off are different [11]. And the differences between the bosonic matrix model and the lattice-regularized Schild model were discussed in [12].…”

“…And the differences between the bosonic matrix model and the lattice-regularized Schild model were discussed in [12]. In our previous paper [11], we proposed a method to estimate the large-N dependences of correlation functions of the IIB matrix model kinematically. We also applied this method to the supersymmetric Schild model with the momentum cut-off and found that it has a different large-N dependence from the IIB matrix model because its action has a different overall factor of N.…”

Representation of SU(∞) Algebra for Matrix Models

“…To construct the representation, however, let us first consider SU(N) algebra in the fundamental representation. We can choose the generators of SU(N) in the following form [11,13,7,14],…”

“…This implies that matrix models could be formulated on the world-sheet with the area-preserving diffeomorphisms. On the other hand, there are some investigations that the bosonic part of the IIB matrix model, which is naively a matrix regularization of the Schild model [10], do not agree with the Schild model in the large N limit [11,12].…”

Noncommutative String Worldsheets from Matrix Models

“…While this work was being completed, we received a preprint[22] where the worldsheet theory(3.4) is discussed from a different point of view.…”