A comment on anti-brane singularities in warped throats

TL;DR

The paper investigates the backreaction of a stack of $p$ anti-D3 branes on the Klebanov--Strassler warped throat by expanding in the small parameter $\gamma = p/M$. It computes the imaginary self-dual (ISD) and imaginary anti-self-dual (IASD) three-form fluxes $G_\pm$ and shows that, at linear order, both exhibit infrared singularities near the brane region, with leading $1/\tau$ behavior. The analysis links these singularities to the SUSY-breaking sector via the modes $\tilde{\xi}^a$ and $\tilde{\phi}^a$, and discusses their interpretation through a $\lambda(\tau)$ parametrization that encodes ISD breaking. By drawing an analogy with anti-D6 backreaction, the work suggests the ISD singularity may persist in the full nonlinear solution, raising questions about the viability of the metastable state and the potential role of brane polarization in resolving the singularity.

Abstract

We compute the imaginary self-dual (ISD) and imaginary anti-self-dual (IASD) fluxes for the Klebanov-Strassler background perturbed by a stack of p anti-D3 branes. We show that, at linear order in p, they both have a singularity in the near-brane region. While one can argue that the IASD flux may disappear at full non-linear level, no such argument exists for the ISD mode. An analogy with anti-D6 backreaction suggests that such singularity may survive once full backreaction is taken into account and may be a universal feature of anti-brane solutions.

Figures (1)

• Figure 1: The ISD flux with legs on $g_3$, $g_4$ and $g_5$ for the Klebanov--Strassler geometry perturbed by anti--D3 branes. The plot is for $P=1,3,6$ (solid, dashed and dotted lines) and $p=1$.