Remarks on the Calculations of Charged Open String Amplitudes: the 1-loop Tadpole

TL;DR

This paper constructs the 1-loop tadpole amplitude for charged open bosonic strings in an external electromagnetic field, addressing the complexities introduced by shifted moding in such scenarios.

Contribution

It provides an explicit operator formalism construction of the 1-loop tadpole for charged open strings, a foundational step for loop amplitude calculations in these contexts.

Findings

Explicit formula for the 1-loop tadpole in charged open strings

Addresses challenges of shifted moding in string interactions

Provides a basis for general loop amplitude construction

Abstract

In string theory, there are various physical situations where the world-sheet fields have a shifted moding. For instance, this is the case for the twisted closed string in Z_N orbifold or for the charged open string in a constant electro-magnetic field. Because of this feature, it is quite challenging to give explicit formulae describing the string interaction, even for the bosonic case. In this note, we focus on the case of the charged open bosonic string and construct the 1-loop tadpole which is an object generating all 1-point functions from the annulus in the presence of an external field. In the operator formalism, this represents one of the basic building blocks for the construction of a general loop amplitude.