New Handles for String Scattering Amplitudes

Introduction

String Theory is currently the only known theoretical framework that unifies the concepts of quantum mechanics and gravity in a consistent way. As such, it makes concrete quantitative predictions for the interaction of gravitons in the form of scattering amplitudes. Unfortunately, the technical complexity of the theory is staggering, and most attempts to directly compute such scattering amplitudes beyond the leading orders have been stifled by technical difficulties.

Project Goals

This project aims to overcome these difficulties by applying three new and unconventional tools to the problem. StringScats's three-pronged strategy leverages:

1. Numerical techniques
2. Saddle-point approximation
3. Exact evaluation techniques such as the Hardy-Littlewood circle method

It seeks to crack the necessary hard computations in string perturbation theory and obtain a long-sought glimpse into the quantum properties of gravity.

Potential Rewards

Among the numerous potential rewards, we would, for the first time ever, get a direct handle on the analytic structure of a quantum gravity amplitude and understand the very high energy behavior of String Theory and how it interacts with the UV-finiteness of the theory.

Broader Implications

StringScat will also have ramifications in neighboring fields such as:

• Black hole physics
• S-matrix bootstrap
• Number theory
• The geometry of the moduli space of Riemann surfaces that features prominently in the calculation

Importance of Scattering Amplitudes

Scattering amplitudes represent one of the handful of accessible windows into quantum gravity and hence offer great potential for tangible progress in the subject. Despite the enormous importance of this topic in physics, it has received far too little attention.

Recent Advances

Recent advances in the understanding of formal aspects of the string perturbation theory, developments of numerical methods, and the increasing synthesis of the subject with mathematics now permit us to attack the problem in earnest.