On the Generalized Gluing and Resmoothing Theorem

Details On the Generalized Gluing and Resmoothing Theorem On the Generalized Gluing and Resmoothing Theorem

1998-05-19

arxiv.org/abs/hep-th/9805119v1

Prog.Theor.Phys. 100 (1998) 437-454

Physics

High Energy Physics

High Energy Physics - Theory

19 pages, LaTeX with PTPTeX.sty, 3 eps figures

Scientific paper

10.1143/PTP.100.437

The generalized gluing and resmoothing theorem originally proved by LeClair, Peskin and Preitschopf, gives a powerful formula for the fused vertex obtained by contracting any two vertices in string field theories. Although the theorem is naturally expected to hold for the vertices at any loop level, the original proof was restricted to the vertices at tree level. Here we present a simplified proof for the tree level theorem and then prove explicitly the extended version at one-loop level. We also find that a non-trivial sign factor, which depends on the string states to be contracted, appears in the theorem. This sign factor turns out to be essential for reproducing correctly the conformal field theory correlation function on the torus.

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