String/$(D-5)$-brane Duality and $S$ Duality as Symmetries of Actions

TL;DR

This paper demonstrates how string/$(D-5)$-brane duality and $S$ duality can be realized at the action level in heterotic string theory, using Lagrange multipliers and double dualization techniques.

Contribution

It provides a method to implement dualities directly at the action level, linking elementary and solitonic solutions through a dual dictionary.

Findings

Duality between heterotic string and $(D-5)$-brane actions established.

$S$ duality reconstructed as double dualization in compactified heterotic string.

A dual dictionary for translating solutions is constructed.

Abstract

We realize the string/$(D-5)$-brane duality on the action level between the $T^{10-D}$-compactified heterotic string effective action and the $(D-5)$- brane effective action in $D$ dimensions by managing a Lagrange multiplier field. A dual dictionary is composed to be available for the translation between the elementary or solitonic solutions of the dual pair of actions. In the same way the $S$ duality is also reconstructed on the action level as a double dualization for the $T^6$-compactified heterotic string effective action.