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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 compellinginterpretation as near-horizon limits of $(p,q)$ 5-brane webs, and thepunctures have been interpreted as additional 7-branes in the web. In this workwe provide further support for this interpretation and clarify several aspectsof the identification of the supergravity solutions with brane webs. To furthersupport the identification of the punctures with 7-branes, we show thatpunctures with infinitesimal monodromy match a probe 7-brane analysis using$\kappa$-symmetry. We then construct families of solutions with fixed 5-branecharges and punctures with finite monodromy, corresponding to fully backreacted7-branes. We compute the sphere partition functions of the dual 5d SCFTs anduse the results to discuss concrete brane web interpretations of thesupergravity solutions.

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