Field Theory Expansions of String Theory Amplitudes.

Area of Science:

• Theoretical Physics
• High Energy Physics
• Mathematical Physics

Background:

• Standard series representations of Euler-Beta functions and string amplitudes lack desired analytic properties.
• Quantum field theory (QFT) provides a framework for understanding fundamental interactions and amplitudes.

Purpose of the Study:

• To develop new, QFT-inspired representations for Euler-Beta functions and tree-level string amplitudes.
• To incorporate analytic properties like poles and contact interactions, crucial in QFT.

Main Methods:

• Utilized a novel two-channel, local, crossing symmetric dispersion relation.
• Applied mass-level truncation to preserve amplitude features.
• Demanded QFT-like properties to identify specific amplitudes.

Main Results:

• Achieved analytic representations of Euler-Beta functions and string amplitudes, valid beyond poles.
• Successfully singled out the open superstring amplitude by imposing QFT-like conditions.
• Demonstrated the challenges in deforming string amplitudes and identified interesting deformations with level truncation.
• Derived new, rapidly converging parametric representations for the Zeta function and π.

Conclusions:

• The new dispersion relation approach offers a QFT-consistent framework for analyzing string amplitudes and related functions.
• Mass-level truncation is a viable technique for preserving essential amplitude characteristics.
• The study yields novel mathematical tools with potential applications in theoretical physics and number theory.