Interacting Intersections

TL;DR

This paper reframes lower-dimensional multi-charge p-branes as the dimensional reductions of higher-dimensional intersecting p-branes with coordinate-dependent harmonic functions. By introducing interacting harmonic functions through KK oxidation and Fourier expansion along compact dimensions, the authors show that pair-wise and multi-intersections exist beyond the standard independent-harmonic-function ansatz, with no-force conditions appearing only in special decoupled cases. Supersymmetry analyses via uplifting to D=11 reveal that the preserved fractions match those of the conventional solutions (e.g., 1/4 for two-function and 1/8 for three-function intersections). The work argues that lower-dimensional bound-state interpretations are only approximate at large distances, while the full higher-dimensional picture encodes intrinsic interactions that bind the constituent branes, offering a broader framework for extremal brane solutions in string/M-theory.

Abstract

Intersecting p-branes can be viewed as higher-dimensional interpretations of multi-charge extremal p-branes, where some of the individual p-branes undergo diagonal dimensional oxidation, while the others oxidise vertically. Although the naive vertical oxidation of a single p-brane gives a continuum of p-branes, a more natural description arises if one considers a periodic array of p-branes in the higher dimension, implying a dependence on the compactification coordinates. This still reduces to the single lower-dimensional p-brane when viewed at distances large compared with the period. Applying the same logic to the multi-charge solutions, we are led to consider more general classes of intersecting p-brane solutions, again depending on the compactification coordinates, which turn out to be described by interacting functions rather than independent harmonic functions. These new solutions also provide a more satisfactory interpretation for the lower-dimensional multi-charge p-branes, which otherwise appear to be nothing more than the improbable coincidence of charge-centres of individual constituents with zero binding energy.