String Scattering Amplitudes and Deformed Cubic String Field Theory

Abstract

We study string scattering amplitudes by using the deformed cubic string field theory which is equivalent to the string field theory in the proper-time gauge. The four-string scattering amplitudes with three tachyons and an arbitrary string state are calculated. The string field theory yields the string scattering amplitudes evaluated on the world sheet of string scattering whereas the coventional method, based on the first quantized theory brings us the string scattering amplitudes defined on the upper half plane. For the highest spin states, generated by the primary operators, both calculations are in perfect agreement. In this case, the string scattering amplitudes are invariant under the conformal transformation, which maps the string world sheet onto the upper half plane. If the external string states are general massive states, generated by non-primary field operators, we need to take into account carefully the conformal transformation between the world sheet and the upper half plane. We show by an explicit calculation that the string scattering amplitudes calculated by using the deformed cubic string field theory transform into those of the first quantized theory on the upper half plane by the conformal transformation, generated by the Schwarz-Christoffel mapping.

12 pages, 2 figures, references added

References in corpus (7)

• New Relations for Gauge-Theory Amplitudes
• Minimal Basis for Gauge Theory Amplitudes
• Notes on High Energy Limit of Bosonic Closed String Scattering Amplitudes
• Deformation of the Cubic Open String Field Theory
• The Appell Function $F_1$ and Regge String Scattering Amplitudes
• Covariant Open String Field Theory on Multiple $Dp$-Branes
• Yang-Mills Gauge Conditions from Witten's Open String Field Theory

Cited by in corpus (9)

• Covariant Open String Field Theory on Multiple $Dp$-Branes
• Solving Lauricella String Scattering Amplitudes through Recurrence Relations
• Four-Gauge-Particle Scattering Amplitudes and Polyakov String Path Integral in the proper-time gauge
• Gravitational Scattering Amplitudes and Closed String Field Theory in the Proper-Time Gauge
• The exact SL(K+3,C) symmetry of string theory
• Quantum deformation of cubic string field theory
• NSR Open Super-string in the proper-time gauge I: Free Field Theory
• Witten's Cubic Open String Field Theory on multiple $Dp$-branes
• BRST Ghost-Vertex Operator in Witten's Cubic Open String Field Theory on Multiple $Dp$-branes