Feynman rules for string field theories with discrete target space

Abstract

We derive a minimal set of Feynman rules for the loop amplitudes in unitary models of closed strings, whose target space is a simply laced (extended) Dynkin diagram. The string field Feynman graphs are composed of propagators, vertices (including tadpoles) of all topologies, and leg factors for the macroscopic loops. A vertex of given topology factorizes into a fusion coefficient for the matter fields and an intersection number associated with the corresponding punctured surface. As illustration we obtain explicit expressions for the genus-one tadpole and the genus-zero four-loop amplitude.

19 pages, harvmac, 4 uuencoded figures included using epsf. A missing term added to the expression for the genus-one tadpole and Fig.3 modified correspondingly

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• Boundary Ground Ring in 2D String Theory
• Non-Rational 2D Quantum Gravity II. Target Space CFT
• Matrix models as conformal field theories: genus expansion
• Boundary operators and touching of loops in 2d gravity