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

T. Nakatsu
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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.

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T. Nakatsu. 2002-12-03. Classical Open-String Field Theory ; $A_{\infty}$-Algebra, Renormalization Group and Boundary States. https://doi.org/10.1016/s0550-3213(02)00495-9

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