Fully Localized Brane Intersections - The Plot Thickens

TL;DR

This paper investigates fully localized intersecting brane solutions in supergravity, revealing that perturbation theory breaks down for certain low-dimensional branes, suggesting possible non-existence of such solutions in those cases.

Contribution

It develops a perturbative method for constructing localized intersecting brane solutions and identifies cases where perturbation theory fails, indicating fundamental differences in solution behavior.

Findings

Perturbation theory breaks down at second order for M2 and Dp branes with p ≤ 3.

Perturbation theory remains well-behaved for higher p-branes at this order.

Full non-linear solutions may not exist for p ≤ 3, affecting the understanding of brane intersections.

Abstract

We study fully localized BPS brane solutions in classical supergravity using a perturbative approach to the coupled Born-Infeld/bulk supergravity system. We derive first order bulk supergravity fields for world-volume solitons corresponding to intersecting M2-branes and to a fundamental string ending on a D3-brane. One interesting feature is the appearance of certain off-diagonal metric components and corresponding components of the gauge potentials. Making use of a supersymmetric ansatz for the exact fields, we formulate a perturbative expansion which applies to $M2 \perp M2 (0), M5 \perp M5 (3)$ and $Dp \perp Dp (p-2)$ intersections. We find that perturbation theory qualitatively distinguishes between certain of these cases: perturbation theory breaks down at second order for intersecting M2-branes and D$p$-branes with $p\le 3$ while it is well behaved, at least to this order, for the remaining cases. This indicates that the behavior of the full non-linear intersecting Dp-brane solutions may be qualitatively different for $p \le 3$ than for $p \ge 4$, and that fully localized asymptotically flat solutions for $p \le 3$ may not exist. We discuss the consistency of these results with world-volume field theory properties.