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

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

2001-05-28

arxiv.org/abs/hep-th/0105272v4

Nucl.Phys. B642 (2002) 13-90

Physics

High Energy Physics

High Energy Physics - Theory

91 pages, 17 figures. This is the published version. Section 1 (Introduction) is revised to include a brief review on renormal

Scientific paper

10.1016/S0550-3213(02)00495-9

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.

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