# On the multiloop soft theorem of the dilaton in the bosonic string

## TL;DR

This paper demonstrates that using Arakelov's Green function in the closed bosonic string ensures consistent factorization of multiloop scattering amplitudes with a soft dilaton emission, extending previous one-loop results to all loops.

## Contribution

It introduces a multiloop Green function choice that guarantees amplitude factorization with a soft dilaton, revealing a high-energy symmetry in bosonic string theory.

## Key findings

- Factorization holds at all loop orders for soft dilaton emissions.
- Arakelov's Green function is key to maintaining amplitude consistency.
- High-energy quantum symmetry protects amplitude structure.

## Abstract

In this note we show that by fixing the multiloop Green function in the closed bosonic string to be Arakelov's Green function, one obtains factorization of scattering amplitudes with a softly emitted dilaton to the same level as with a graviton to all loop order. This extends our previous analysis at one loop to all loop orders and confirms that some high-energy quantum symmetry in the bosonic string protects the factorization of amplitudes with softly emitted dilatons.