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 conventional 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.
Highlights
String theory was formulated first in terms of the scattering amplitude, which is known as Veneziano amplitude [1]
We applied the deformed cubic bosonic open string field theory to the four-string scattering amplitudes with three tachyons and one general string state, which are the main objects of the recent studies on the high-energy symmetries of string theory
String scattering amplitudes have been calculated in the previous works mostly by using the first quantized string theory
Summary
String theory was formulated first in terms of the scattering amplitude, which is known as Veneziano amplitude [1]. The Veneziano amplitude was soon generalized to the Virasoro-Shapiro amplitude [2, 3] These scattering amplitudes marked the birth of the string theory. In the first quantized theory, we may obtain the string scattering amplitudes by evaluating the Polyakov string path integral with vertex operators inserted on the string world sheet. By using the deformed cubic string field theory [13], we will calculate the four-string scattering amplitudes with three tachyons and an arbitrary string states, which have been extensively studied in Refs. In recent works [13, 27], one of the authors showed that the non-planar world sheets of Witten’s cubic open string field theory [28, 29] can be made planar if we choose the external string states judiciously. The deformed cubic string field theory, which is equivalent to the covariant string field theory in the proper-time gauge [30], has a number of
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