Classical Open-String Field Theory ; $A_{\infty }$-Algebra, Renormalization Group and Boundary States

Abstract

We investigate classical bosonic open-string field theory from the perspective of the Wilson renormalization group of world-sheet theory. The microscopic action is identified with Witten's covariant cubic action and the short-distance cut-off scale is introduced by length of open-string strip which appears in the Schwinger representation of open-string propagator. {\it Classical open-string field theory} in the title means open-string field theory governed by a classical part of the low energy action. It is obtained by integrating out suitable tree interactions of open-strings and is of non-polynomial type. We study this theory by using the BV formalism. It turns out to be deeply related with deformation theory of $A_{\infty }$-algebra. We introduce renormalization group equation of this theory and discuss it from several aspects. It is also discussed that this theory is interpreted as a boundary open-string field theory. Closed-string BRST charge and boundary states of closed-string field theory in the presence of open-string field play important roles.

91 pages, 17 figures. This is the published version. Section 1 (Introduction) is revised to include a brief review on renormalization group. Other parts do not change

References in corpus (2)

• Introduction to string field theory
• Some computation on g Function and Disc Partition Function and Boundary String Field Theory

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