Lectures on Scattering Amplitudes in String Theory

TL;DR

This paper provides an overview of calculating scattering amplitudes in bosonic string theory, highlighting their significance for understanding string theory's UV behavior and its relation to gravity.

Contribution

It offers a detailed explanation of the Polyakov path integral, gauge symmetries, and the derivation of basic string scattering amplitudes in bosonic open string theory.

Findings

Connection between string scattering amplitudes and UV properties of string theories

Derivation of simple scattering amplitudes using Riemann surfaces

Insights into gauge symmetries in the Polyakov path integral

Abstract

In these lecture notes, we take a closer look at the calculation of scattering amplitudes for the bosonic string. It is believed that string theories form the UV completions of (super)gravity theories. Support for this claim can be found in the (on-shell) scattering amplitudes of strings. On the other hand, studying these string scattering amplitudes opens a window on the UV behavior of the string theories themselves. In these short set of lectures, we discuss the two-dimensional Polyakov path integral for the string, and its gauge symmetries, the connection to Riemann surfaces and how to obtain some of the simplest string scattering amplitudes. We end with some comments on more advanced topics. For simplicity we limit ourselves to bosonic open string theory in 26 dimensions.