Type IIB 7-branes in warped $AdS_6$: partition functions, brane webs and probe limit

TL;DR

This paper investigates Type IIB supergravity solutions with warped $AdS_6$ spaces, exploring their interpretation as 5-brane webs with 7-branes, and computes dual 5d SCFT partition functions to support this correspondence.

Contribution

It provides new supergravity solutions with punctures representing 7-branes and clarifies their relation to brane web configurations, including probe and backreacted cases.

Findings

Punctures with infinitesimal monodromy match probe 7-brane analysis.

Constructed solutions with finite monodromy correspond to fully backreacted 7-branes.

Computed sphere partition functions of dual 5d SCFTs supporting brane web interpretations.

Abstract

We study Type IIB supergravity solutions with spacetime of the form $AdS_6\times S^2$ warped over a Riemann surface $\Sigma$, where $\Sigma$ includes punctures around which the supergravity fields have non-trivial $SL(2,R)$ monodromy. Solutions without monodromy have a compelling interpretation as near-horizon limits of $(p,q)$ 5-brane webs, and the punctures have been interpreted as additional 7-branes in the web. In this work we provide further support for this interpretation and clarify several aspects of the identification of the supergravity solutions with brane webs. To further support the identification of the punctures with 7-branes, we show that punctures with infinitesimal monodromy match a probe 7-brane analysis using $\kappa$-symmetry. We then construct families of solutions with fixed 5-brane charges and punctures with finite monodromy, corresponding to fully backreacted 7-branes. We compute the sphere partition functions of the dual 5d SCFTs and use the results to discuss concrete brane web interpretations of the supergravity solutions.