A classification of long-range interactions between two stacks of $p$ \& $p'$-branes

TL;DR

This paper classifies the long-range interactions between two stacks of p- and p'-branes, extending previous work to non-parallel configurations, and provides explicit examples to understand their attractive or repulsive nature.

Contribution

It generalizes the computation of brane interactions to non-parallel stacks and classifies their interaction types, aiding the understanding of complex brane systems.

Findings

Interaction nature depends on brane configuration

Classification covers parallel and non-parallel cases

Explicit examples demonstrate the classification

Abstract

We generalize the computations of the long-range interactions between two parallel stacks of branes in \cite{Wu and Wang, Prof. Lu's lecture notes} to various cases when two stacks of branes are not placed parallel to each other. We classify the nature of interaction (repulsive or attractive) for each special case and this classification can be used to justify the nature of long-range interaction between two complicated brane systems such as brane bound states. We will provide explicit examples in this paper to demonstrate this.