Non-Abelian (p,q) Strings in the Warped Deformed Conifold

TL;DR

This paper computes the tension of (p,q)-strings in a warped deformed conifold using a non-Abelian DBI approach, revealing detailed flux-dependent behavior and corrections that challenge simple scaling assumptions.

Contribution

It provides an exact calculation of (p,q)-string tensions in a warped conifold and proposes a general tension formula for arbitrary (p,q) values.

Findings

Agreement with previous results up to order 1/M^2

Proposed general tension expression for any (p,q)

Corrections scale as 1/M^2, inconsistent with Casimir scaling

Abstract

We calculate the tension of $(p,q)$-strings in the warped deformed conifold using the non-Abelian DBI action. In the large flux limit, we find exact agreement with the recent expression obtained by Firouzjahi, Leblond and Henry-Tye up to and including order $1/M^2$ terms if $q$ is also taken to be large. Furthermore using the finite $q$ prescription for the symmetrised trace operation we anticipate the most general expression for the tension valid for any $(p,q)$. We find that even in this instance, corrections to the tension scale as $1/M^2$ which is not consistent with simple Casimir scaling.