Reduction of open string amplitudes by mostly BRST exact operators

Shigenori Seki,Tomohiko Takahashi

doi:10.1016/j.physletb.2021.136664

Shigenori Seki, Tomohiko Takahashi

Open Access

https://doi.org/10.1016/j.physletb.2021.136664

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Abstract

We study two and three-point tree-level amplitudes of open strings. These amplitudes are reduced from higher-point correlation functions by using mostly BRST exact operators for gauge fixing. For simplicity, we focus on an open string tachyon. The two-point amplitude of open string tachyons is reduced from a three-point function of two tachyon vertex operators and one mostly BRST exact operator. Similarly the three-point amplitude is from a four-point function of three tachyon vertex operators and one mostly BRST exact operator. One can also obtain the two-point amplitude from the four-point function of two tachyon vertex operators and two mostly BRST exact operators. In these derivation from four-point functions, moduli integrals are significant. We discuss the overall signs of amplitudes which are indefinite in this formalism.

Highlights

We study two and three-point tree-level amplitudes of open strings
A mostly BRST exact operator is constructed in the pure spinor formalism of superstring theory [3], and two-point superstring amplitudes have been found to agree with the corresponding expression in the field theories
We have shown that the two and three-point tree-level amplitudes of open string tachyons are reduced from the three and four-point correlation functions by inserting the mostly BRST exact operators E

Summary

12 August 2021

We will find that, after the q-integration, the conventional expression of three-point amplitudes is derived from the additional insertion of the gauge fixing vertex. We will show that conventional open string amplitudes can be reproduced by using our gauge fixing operator for P SL(2, R), except the overall sign which can be positive, negative or zero. This result justifies our gauge fixing procedure of P SL(2, R) and the interpretation of the overall sign in terms of the intersection.

Two-point amplitude from three-point function

Three-point amplitude from four-point function

Overall sign of amplitudes

Two-point amplitude from four-point function

Concluding remarks