Emergent Worldsheet for the AdS Virasoro-Shapiro Amplitude

Area of Science:

• High energy physics
• String theory
• Quantum field theory

Background:

• The Virasoro-Shapiro amplitude describes scattering in string theory.
• Understanding curvature corrections is crucial for refining theoretical models.
• Previous calculations lacked a manifestly single-valued representation for coefficients.

Purpose of the Study:

• To construct an integral representation for the first anti-de Sitter (AdS) curvature correction to the Virasoro-Shapiro amplitude.
• To derive a manifestly single-valued representation for Wilson coefficients in the low-energy expansion.

Main Methods:

• Integral representation over the Riemann sphere.
• Insertion of single-valued multiple polylogarithms of weight three into the flat-space integrand.
• Analysis of the low-energy expansion of the constructed amplitude.

Main Results:

• A novel integral representation for the AdS curvature correction to the Virasoro-Shapiro amplitude was established.
• The integrand incorporates single-valued multiple polylogarithms, ensuring a manifestly single-valued result.
• An elegant representation for Wilson coefficients in the low-energy expansion was obtained.

Conclusions:

• The developed integral representation provides a powerful tool for studying curvature corrections in string theory amplitudes.
• This work offers a more streamlined approach to calculating and understanding Wilson coefficients.
• The findings contribute to a deeper understanding of quantum gravity in curved spacetimes.