Reconstructing a bijection on the level of Le diagrams

TL;DR

This paper provides a combinatorial description of the T-duality map in string theory at the level of Le diagrams, clarifying the dimension shift and offering a new perspective on the bijection.

Contribution

It introduces a novel combinatorial framework for the T-duality map using Le diagrams, enhancing understanding of its structural properties.

Findings

Dimension shift under the T-duality map is clarified

A bijection is reconstructed at the level of Le diagrams

The combinatorial perspective simplifies understanding of the T-duality map

Abstract

Lukowiski, Parisi, and Williams formulated the T-duality map of string theory at a purely combinatorial level as a map on decorated permutations. We combinatorially describe this map at the level of Le diagrams. This perspective makes the dimension shift under the map more transparent.