$AdS_6$ T-duals and Type IIB $AdS_6\times S^2$ Geometries with 7-Branes

TL;DR

This paper demonstrates that known $AdS_6$ backgrounds in Type IIB supergravity, obtained via T-duality from massive IIA solutions, fit within a broader classification of $AdS_6 imes S^2$ geometries with 7-branes warped over Riemann surfaces, providing explicit examples.

Contribution

It extends the classification of $AdS_6 imes S^2$ solutions to include T-dual backgrounds, illustrating their geometric and brane configurations within a unified framework.

Findings

Explicit $AdS_6$ solutions with 7-branes are constructed via Abelian and non-Abelian T-duality.

The Abelian T-dual solution corresponds to an annulus-shaped Riemann surface with D7/O7-branes.

The non-Abelian T-dual solution arises from the upper half-plane geometry.

Abstract

We show that the first $AdS_6$ backgrounds in Type IIB supergravity known in the literature, namely those constructed via T-duality from the Brandhuber-Oz solution to massive IIA, fit within an extension of the global $AdS_6 \times S^2$ solutions with 7-branes warped over a Riemann surface $\Sigma$, recently classified by D'Hoker, Gutperle and Uhlemann, that describes delocalised 5-branes and 7-branes. The solution constructed through Abelian T-duality provides an explicit example of a Riemann surface with the topology of an annulus, that includes D7/O7-branes. In turn, the solution generated through non-Abelian T-duality arises from the upper half-plane.