Proposals on nonperturbative superstring interactions

TL;DR

The work investigates whether nonperturbative M(atrix) theory can realize perturbative superstring sectors, proposing that strings, including longer ones, are embedded in block-diagonal $U(N)$ matrices and that permutation symmetry is encoded in the gauge structure. It introduces a mechanism of representing longer strings via cycles in eigenvector permutations (screwing strings to matrices) and derives the scaling $R_1 \approx \lambda^{2/3}$ (equivalently $\lambda \propto R_1^{3/2}$) between the compactification radius and the coupling, supporting a nonperturbative link between M(atrix) theory and IIA strings. The paper also discusses T-duality, heterotic and type I constructions, and open-string sectors with gauge groups such as $SO(16)\times SO(16)$, while acknowledging unresolved questions about background independence and a covariant, background-independent formulation. Overall, it outlines a framework in which nonperturbative matrix dynamics potentially unifies several superstring theories and illuminates the nonperturbative underpinnings of their perturbative limits.

Abstract

We show a possibility that the matrix models recently proposed to explain (almost) all the physics of M-theory may include the superstring theories that we know perturbatively. The ``1st quantized'' physical system of one IIA string seems to be an exact consequence of M(atrix) theory with a proper mechanism to mod out a symmetry. The central point of the paper is the representation of strings with P^+/epsilon greater than one. I call the mechanism ``screwing strings to matrices''. I also give the first versions of the proof of 2/3 power law between the compactification radius and the coupling constant in this formulation. Multistring states are involved in a M(atrix) theory fashion, replacing the 2nd quantization that I briefly review. We shortly discuss the T-dualities, type I string theory and involving of FP ghosts to all the systems including the original one of Banks et al.