Abstract
We introduce a two parameter family of string field theory vertices, which we refer to as hyperbolic Kaku vertices. It is defined in terms of hyperbolic metrics on the Riemann surface, but the geometry is allowed to depend on inputs of the states. The vertices are defined for both open and closed strings. In either case, the family contains the hyperbolic vertices. Then we show that the open string lightcone vertex is obtained as the flat limit of the hyperbolic Kaku vertices. The open string Kaku vertices, which interpolate between the Witten vertex and the open string lightcone vertex, is also obtained as a flat limit. We use the same limit on the case of closed strings to define the closed string Kaku vertices: a one parameter family of vertices that interpolates between the polyhedral vertices — which are covariant, but not cubic — and the closed string lightcone vertex — which is cubic, but not Lorentz covariant.
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Acknowledgments
We thank Ted Erler for suggesting the topic of this work, for useful discussions and for commenting on an earlier draft of the paper. We also thank Tomáš Procházka for useful discussions. UP thanks the Institute of Physics of the Czech Academy of Sciences for their hospitality during development of this work. The work of VB was supported by the Grant Agency of the Czech Republic under the grant EXPRO 20-25775X. The work of UP was supported by FAPESP grant number 2023/00862-4.
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Bernardes, V., Portugal, U. A two parameter family of lightcone-like hyperbolic string vertices. J. High Energ. Phys. 2024, 205 (2024). https://doi.org/10.1007/JHEP07(2024)205
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DOI: https://doi.org/10.1007/JHEP07(2024)205