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

Abstract

Abstract 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 $$ \mathcal{N}=\left(0,2\right) $$ N = 0 2 supersymmetry,wederivethegeneralconditionsonthegeometryforTypeIIB AdS3 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 $$ {\mathcal{Y}}_8^{\tau } $$ Y 8 τ , which is elliptically fibered over a base $$ {\tilde{\mathrm{\mathcal{M}}}}_6 $$ ℳ ˜ 6 . We construct two classes of solutions given in terms of a product ansatz $$ \tilde{{\mathrm{\mathcal{M}}}_6}=\varSigma \times {\mathrm{M}}_4 $$ ℳ 6 ˜ = Σ × M 4 , where Σ is a complex curve and $$ {\tilde{\mathrm{\mathcal{M}}}}_4 $$ ℳ ˜ 4 is locally a Kähler surface. In the first class $$ {\tilde{\mathrm{\mathcal{M}}}}_4 $$ ℳ ˜ 4 is globally a Kähler 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 AdS3 × K3 × ℳ 5 τ , dual to 2d (0, 2) SCFTs, and AdS3 × S 3/Γ × CY 3, 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 $$ \mathcal{N}=\left(2,2\right) $$ 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 AdS5 solutions with varying axio-dilaton, i.e. F-theoretic solutions, that are dual to 4d $$ \mathcal{N}=1 $$ N = 1 SCFTs.