# Open string T-duality in double space

## TL;DR

This paper extends the double space T-duality framework to open strings, demonstrating that gauge fields at string endpoints can be interpreted as coordinate permutations, thus advancing the understanding of open string T-duality.

## Contribution

It introduces a novel interpretation of open string T-duality as coordinate permutations in double space, filling a gap in the existing theoretical framework.

## Key findings

- Open string gauge fields are T-dual to each other.
- Open string T-duality can be interpreted as coordinate permutations.
- The approach unifies open and closed string T-duality in double space.

## Abstract

The role of double space is essential in new interpretation of T-duality and consequently in an attempt to construct M-theory. The case of open string is missing in such approach because until now there have been no appropriate formulation of open string T-duality. In the previous paper [1], we showed how to introduce vector gauge fields $A^N_a$ and $A^D_i$ at the end-points of open string in order to enable open string invariance under local gauge transformations of the Kalb-Ramond field and its T-dual "restricted general coordinate transformations". We demonstrated that gauge fields $A^N_a$ and $A^D_i$ are T-dual to each other. In the present article we prove that all above results can be interpreted as coordinate permutations in double space.