Abstract
We study covariant open bosonic string field theories on multiple Dp-branes by using the deformed cubic string field theory, which is equivalent to string field theory in the proper-time gauge. Constructing the Fock space representations of the three-string vertex and the four-string vertex on multiple Dp-branes, we obtain the field theoretical effective action in the zero-slope limit. On multiple D0-branes, the effective action reduces to the Banks-Fishler-Shenker-Susskind (BFSS) matrix model. We also discuss the relation between open string field theory on multiple D-instantons in the zero-slope limit and the Ishibashi-Kawai-Kitazawa-Tsuchiya (IKKT) matrix model. The covariant open string field theory on multiple Dp-branes could be useful to study the non-perturbative properties of quantum field theories in (p + 1)-dimensions in the framework of the string theory. The non-zero-slope corrections may be evaluated systematically by using covariant string field theory.
Highlights
The string theories are defined only in critical dimensions; 10 dimension for the super-string theories and 26 dimension for the bosonic string theories
We wish to understand the origins of actions for the matrix models [1, 2], which have served as important tools to study the non-perturbative effects of super-string theories and the M -theory [3,4,5] within the framework of the covariant string field theory
We have shown that the deformed cubic open string field theory if defined on the space filling D-brane, yield the non-Abelian Yang-Mills theory in the zero-slope limit
Summary
The string theories are defined only in critical dimensions; 10 dimension for the super-string theories and 26 dimension for the bosonic string theories. The purpose of this work is twofold: First, we shall construct covariant string field theories on Dp-branes of which zero-slope limits correspond to the quantum field theories in dimension lower than the critical dimension. These covariant string field theories will be useful to understand various non-perturbative features of quantum field theories, which could not have been approached by the conventional perturbation theory. We have shown that the deformed cubic open string field theory if defined on the space filling D-brane, yield the non-Abelian Yang-Mills theory in the zero-slope limit.
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