# From the octagon to the SFT vertex - gluing and multiple wrapping

## TL;DR

This paper explores different methods of decomposing and decompactifying the string field theory vertex, demonstrating how gluing via resumming wrapping corrections reproduces exact finite-volume coefficients in pp-wave backgrounds.

## Contribution

It introduces a framework for gluing the octagon to the SFT vertex and emphasizes the importance of multiple wrapping corrections for exact results.

## Key findings

- Gluing the octagon reproduces the decompactified SFT vertex.
- Resumming multiple wrapping corrections is crucial for accuracy.
- Exact finite volume Neumann coefficients are obtained through this method.

## Abstract

We compare various ways of decomposing and decompactifying the string field theory vertex and analyze the relations between them. We formulate axioms for the octagon and show how it can be glued to reproduce the decompactified pp-wave SFT vertex which in turn can be glued to recover the exact finite volume pp-wave Neumann coefficients. The gluing is performed by resumming multiple wrapping corrections. We observe important nontrivial contributions at the multiple wrapping level which are crucial for obtaining the exact results.