Mapping between Witten and Lightcone String Field Theories

Abstract

We propose a transformation between the off-shell field variables of Witten's open bosonic string field theory and the traditional lightcone string field theory of Kaku and Kikkawa, based on Mandelstam's interacting string picture. This is accomplished by deforming the Witten vertex into lightcone cubic and quartic vertices, followed by integrating out the ghost and lightcone oscillator excitations from the string field. Surprisingly, the last step does not alter the cubic and quartic interactions and does not generate effective vertices, and leads precisely to Kaku and Kikkawa's lightcone string field theory.

arXiv comment74 pages, 23 figures. Added appendix on the lightcone SFT action. Simplified discussion of the field transformation and the singular nature of lightcone gauge in generic SFTs, which has been called the "soft string problem."

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• Perturbative path-integral of string field and the $A_{\infty }$ structure of the BV master equation
• Topological defects in nonlocal field theories
• Quantum deformation of cubic string field theory