Towards a Non-perturbative Formulation of IIB Superstrings by Matrix Models

TL;DR

This paper explores a non-perturbative approach to IIB superstring theory using matrix models, demonstrating limitations of the IKKT model and proposing a modified model that reproduces superstring actions at quantum level.

Contribution

It introduces a modified matrix model with an additional Hermitian matrix, enabling the reproduction of the Green-Schwarz action at quantum level, advancing non-perturbative superstring formulations.

Findings

IKKT model matches superstring results at large distances or low velocities

Modified matrix model reproduces Green-Schwarz action quantum mechanically

Proposes a new matrix integration approach similar to Schild's formulation

Abstract

We address the problem of a non-perturbative formulation of superstring theory by means of the recently proposed matrix models. For the model by Ishibashi, Kawai, Kitazawa and Tsuchiya (IKKT), we perform one-loop calculation of the interaction between operator-like solutions identified with D-brane configurations of type IIB superstring (in particular, for parallel moving and rotated static p-branes). Comparing to the superstring calculations, we show that the matrix model reproduces the superstring results only at large distances or small velocities, corresponding to keeping only the lowest mass closed string modes. We propose a modification of the IKKT matrix model introducing an integration over an additional Hermitian matrix required to have positive definite eigenvalues, which is similar to the square root of the metric in the continuum Schild formulation of IIB superstrings. We show that for this new matrix action the Nambu-Goto version of the Green-Schwarz action is reproduced even at quantum level.