(p,q)-strings probing five-brane webs

TL;DR

This paper investigates the behavior of probe (p,q)-strings in supergravity solutions related to five-brane webs, providing evidence for the interpretation of these solutions as near-horizon geometries of five-brane webs and exploring string junction formations.

Contribution

It offers new insights into the correspondence between supergravity solutions and five-brane webs by analyzing probe string embeddings and their relation to string junction tensions.

Findings

Probe (p,q)-string behavior matches brane web predictions.

Minimal energy embeddings often break supersymmetry.

Identified a supergravity quantity linked to junction tension.

Abstract

In recent work, globally well-defined Type IIB supergravity solutions with geometry $AdS_6 \times S^2$ warped over a Riemann surface $\Sigma$ were constructed and conjectured to describe the near-horizon geometry of $(p,q)$ five-brane webs in the conformal limit. In the present paper, we offer more evidence for this interpretation of the supergravity solutions in terms of five-brane webs. In particular, we explore the behavior of probe $(p,q)$-strings in certain families of these $AdS_6 \times S^2\times \Sigma$ backgrounds and compare this behavior to that predicted by microscopic, brane web considerations. In the microscopic picture, we argue that the embedding of a probe string may give rise to the formation of string junctions involving open strings anchored on the branes of the web. We then identify a quantity on the supergravity side that is conjectured to be equivalent to the total junction tension in a class of backgrounds corresponding to brane webs with four semi-infinite external five-branes. In the process, we will show that for general brane web backgrounds, the minimal energy probe string embeddings do not coincide with the embeddings preserving half of the background supersymmetries.