# One Loop Tadpole in Heterotic String Field Theory

## TL;DR

This paper calculates the off-shell 1-loop tadpole amplitude in heterotic string field theory, providing explicit formulas and discussing the role of picture changing operators using homotopy algebra methods.

## Contribution

It introduces a method to compute the 1-loop tadpole exactly in heterotic string field theory with a specific cubic vertex, utilizing homotopy algebra techniques.

## Key findings

- Explicit expressions for Feynman graph decomposition and local coordinate maps
- Demonstration of exact computation of the 1-loop tadpole amplitude
- Analysis of spurious poles and picture changing operator choices

## Abstract

We compute the off-shell 1-loop tadpole amplitude in heterotic string field theory. With a special choice of cubic vertex, we show that this amplitude can be computed exactly. We obtain explicit and elementary expressions for the Feynman graph decomposition of the moduli space, the local coordinate map at the puncture as a function of the modulus, and the $b$-ghost insertions needed for the integration measure. Recently developed homotopy algebra methods provide a consistent configuration of picture changing operators. We discuss the consequences of spurious poles for the choice of picture changing operators.