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

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 the 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. ∗E-mail: [email protected] †E-mail: [email protected] [email protected] ‡E-mail: [email protected] §E-mail: [email protected] ¶E-mail: [email protected]