The Shape of Branes Pulled by Strings

TL;DR

This paper investigates the shape and geometry of D-branes deformed by attached strings, using M-theory and monopole solutions, and confirms the energy matches string tension expectations.

Contribution

It introduces two methods to analyze D-brane spike shapes caused by strings, connecting M-theory embeddings and monopole scalar field configurations.

Findings

The shape of D-brane spikes can be derived from M-theory limits.

The geometry of D3-brane embeddings relates to monopole scalar fields.

Energy calculations align with string and D-string tension predictions.

Abstract

We examine the system where a string stretches between pair of D-branes, and study the bending of the D-brane caused by the tension of the string. If the distance between the pair of D-branes is sent to infinity, the tension of the string stretching between them is strong enough to pull the spike all the way to infinity. We study the shape of these spikes when the branes are finite distance apart using two different methods. First, we consider a string stretched between a pair of D2-branes in type IIA theory by going to the M-theory limit in which all of these branes are M-theory 2-branes embedded along a holomorphic curve. Second, we consider a D-string stretched between a pair of D3-branes in type IIB theory and infer the geometry of the D3-brane embeddings from the configuration of the adjoint scalar field in the magnetic monopole solution of Prasad and Sommerfield. The case of fundamental string stretching between a pair of D3-branes follows from S-duality. The energy of these configurations matches the expected value based on fundamental string and D-string tensions.