T-duality and Noncommutative DBI Action

TL;DR

This paper explores the relationship between T-duality and noncommutative descriptions of the Dirac-Born-Infeld (DBI) action, clarifying how noncommutativity parameters relate to closed string variables in string theory.

Contribution

It provides a detailed analysis of the noncommutative DBI Lagrangian and its T-dual, expressing key parameters in terms of closed string variables and constraining noncommutativity.

Findings

Expressed noncommutativity parameter in terms of closed string variables

Derived relations for effective metric and coupling constants

Clarified the role of the extra modulus in T-dual theories

Abstract

In this article we study the noncommutative description of the DBI Lagrangian and its T-dual counterpart. We restrict the freedoms of the noncommutativity parameters of these Lagrangians. Therefore the noncommutativity parameter, the effective metric, the effective coupling constant of the string and the extra modulus ${\tilde \Phi}$ of the effective T-dual theory, can be expressed in terms of the closed string variables $g$, $B$, $g_s$ and the noncommutativity parameter of the effective theory of open string.