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String Amplitudes from Field-Theory Amplitudes and Vice Versa.

Song He^1,2, Fei Teng³, Yong Zhang^1,2

¹CAS Key Laboratory of Theoretical Physics, Institute of Theoretical Physics, Chinese Academy of Sciences, Beijing 100190, China.

Physical Review Letters

|July 9, 2019

Summary

We developed a method to simplify string correlators into logarithmic functions, enabling field-theory amplitude calculations using the Cachazo-He-Yuan (CHY) formula. This technique reveals string amplitudes as a double copy of field-theory amplitudes and specific integrals.

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Area of Science:

Theoretical Physics
High Energy Physics
String Theory

Background:

String theory amplitudes are complex to compute.
The Cachazo-He-Yuan (CHY) formula provides a powerful framework for calculating scattering amplitudes in field theory.
Relating string theory and field theory amplitudes is a key goal in theoretical physics.

Purpose of the Study:

To present a novel integration-by-parts reduction for massless tree-level string correlators.
To establish a connection between string amplitudes and field-theory amplitudes via the CHY formula.
To derive a closed-form CHY integrand for specific quantum field theories.

Main Methods:

Employing integration-by-parts reduction techniques on string correlators.
Utilizing the Cachazo-He-Yuan (CHY) formula to define field-theory amplitudes.
Applying the developed method to open bosonic and heterotic string theories.

Main Results:

Any massless tree-level string correlator can be reduced to an equivalence class of logarithmic functions.
String amplitudes are shown to be the double copy of field-theory amplitudes and a special disk or sphere integral.
A closed-form CHY integrand is obtained for the (DF)^2 + Yang-Mills + phi^3 theory.

Conclusions:

The presented method offers a generic approach applicable to any rational correlator with the correct SL(2) weight.
This work provides a new pathway for understanding the relationship between string theory and quantum field theory.
The derived CHY integrand simplifies calculations for specific, important quantum field theories.