F-theory and AdS3/CFT2 (2, 0)

We continue to develop the program initiated in [ 1] of studying supersymmetric AdS3 backgrounds of F-theory and their holographic dual 2d superconformal field theories, which are dimensional reductions of theories with varying coupling. Imposing 2d N = (0, 2) supersymmetry, we derive the general conditions on the geometry for Type IIB AdS 3 solutions with varying axio-dilaton and five-form flux. Locally the compact part of spacetime takes the form of a circle fibration over an eight-fold Y τ8 , which is elliptically fibered over a base M!6. We construct two classes of solutions given in terms of a product ansatz M!6 = Σ × M 4, where Σ is a complex curve and M 4 is locally a K¨ahler surface. In the first class M 4 is globally a K¨ahler surface and we take the elliptic fibration to vary non-trivially over either of these two factors, where in both cases the metrics on the total space of the elliptic fibrations are not Ricci-flat. In the second class the metric on the total space of the elliptic fibration over either curve or surface are Ricci-flat. This results in solutions of the type AdS 3 × K3 × M τ5, dual to 2d (0 , 2) SCFTs, and AdS 3 × S 3 / Γ × CY3 , dual to 2d (0 , 4) SCFTs, respectively. In all cases we compute the charges for the dual field theories with varying coupling and find agreement with the holographic results. We also show that solutions with enhanced 2d N = (2 , 2) supersymmetry must have constant axio-dilaton. Allowing the internal geometry to be non-compact leads to the most general class of Type IIB AdS 5 solutions with varying axio-dilaton, i.e. F-theoretic solutions, that are dual to 4d N = 1 SCFTs.