On the Stability of D7 - anti-D7 Probes in Near-conformal Backgrounds

TL;DR

This paper analyzes the perturbative stability of a nonsupersymmetric D7-anti-D7 brane embedding in near-conformal backgrounds, confirming the presence of a tachyonic mode and discussing potential stabilization methods.

Contribution

It introduces a new analytical approach with an improved coordinate system to accurately determine the fluctuation spectrum of the brane embedding.

Findings

Confirmed the existence of a normalizable tachyonic mode.

Reproduced previous numerical results with an analytical method.

Discussed potential stabilization via worldvolume flux.

Abstract

We investigate the perturbative stability of a nonsupersymmetric D7 - anti-D7 brane embedding in a particular class of type IIB backgrounds. These backgrounds are the gravitational duals of certain strongly-coupled gauge theories, that exhibit a nearly conformal regime (known as a walking regime). Previous studies in the literature have led to conflicting results as to whether the spectrum of fluctuations around the flavor D7 - anti-D7 embedding has a tachyonic mode or not. Here we reconsider the problem with a new analytical method and recover the previously obtained numerical results. We also point out that the earlier treatments relied on a coordinate system, in which it was not possible to take into account fluctuations of the point of confluence of the D7 - anti-D7 branes. Using an improved coordinate system, we confirm the presence of a normalizable tachyonic mode in this model, in agreement with the numerical calculations. Finally, we comment on the possibility of turning on worldvolume flux to stabilize the probe branes configuration.