Computing in string field theory using the Moyal star product

Itzhak Bars and Yutaka Matsuo
Phys. Rev. D 66, 066003 – Published 17 September 2002
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Abstract

Using the Moyal star product, we define open bosonic string field theory carefully, with a cutoff, for any number of string oscillators and any oscillator frequencies. Through detailed computations, such as Neumann coefficients for all string vertices, we show that the Moyal star product is all that is needed to give a precise definition of string field theory. The formulation of the theory as well as the computation techniques are considerably simpler in the Moyal formulation. After identifying a monoid algebra as a fundamental mathematical structure in string field theory, we use it as a tool to compute with ease the field configurations for wedge, sliver, and generalized projectors, as well as all the string interaction vertices for perturbative as well as monoid-type nonperturbative states. Finally, in the context of VSFT we analyze the small fluctuations around any D-brane vacuum. We show quite generally that to obtain nontrivial mass and coupling, as well as closed strings, there must be an associativity anomaly. We identify the detailed source of the anomaly, but leave its study for future work.

  • Received 15 June 2002

DOI:https://doi.org/10.1103/PhysRevD.66.066003

©2002 American Physical Society

Authors & Affiliations

Itzhak Bars*

  • CIT-USC Center for Theoretical Physics, Department of Physics and Astronomy, University of Southern California, Los Angeles, California 90089-2535

Yutaka Matsuo

  • Department of Physics, University of Tokyo, Hongo 7-3-1, Bunkyo-ku, Tokyo 113-0033, Japan

  • *Electronic address: bars@usc.edu
  • Electronic address: matsuo@phys.s.u-tokyo.ac.jp

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Vol. 66, Iss. 6 — 15 September 2002

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