Warped AdS6 x S2 in Type IIB supergravity I: local solutions
A bstractWe investigate the existence of solutions with 16 residual supersymmetries to Type IIB supergravity on a space time of the formc AdS6xS2 warped over a two dimensional Riemann surface S. The SO(2, 5) x SO(3) isometry extends to invariance under the exceptional Lie superalgebra F (4) In the present paper, we construct the general Ansatz compatible with these symmetries, derive the corresponding reduced BPS equations, and obtain their complete local solution in terms of two locally holomorphic functions A+ \mathcal{A}}_{\pm on S, subject to certain positivity and regularity conditions. Globally, (A+ \mathcal{A}}_{ ,A \mathcal{A}}_{ are allowed to be multiple valued on S and be holomorphic sections of a holomorphic bundle over S with structure group contained in SU11xC$ \mathrm{S}\mathrm{U}\left(1,1\right)\times \mathbb{C} Globally regular solutions are expected to provide the near horizon geometry of (p, q) 5 brane and 7 brane webs which are holographic duals to five dimensional conformal field theories. A preliminary analysis of the positivity and regularity conditions will be presented here, leaving the construction of globally regular solutions to a subsequent paper.