Holographic F-theory

Abstract

The central theme of this thesis is Type IIB supergravity solutions and their field theory duals. The uniqueness of our set up is the inclusion of an AdS factor in the geometry. In traditional F-theory compactifications the non-compact part of spacetime is Minkowski space, by including an AdS factor we may appeal to the AdS/CFT correspondence and probe the dual field theories from the gravity side. In the first part of this thesis we will be interested in AdS3 solutions with F-theoretic interpretations. We find the general conditions for the existence of a su-persymmetric solution with (0, 2) supersymmetry. This is determined by the choice of a 6d K¨ahler base satisfying a master equation. One may give this equation an F-theoretic interpretation by the inclusion of an auxiliary elliptic fibration which models the varying axio-dilaton as in canonical F-theory compactifications. The unique family of (0, 4) solutions are holographically dual to D3-branes wrapped on curves inside a Calabi–Yau three-fold and correspond to self-dual strings in the 6d N = (0, 1) theory obtained from F-theory on the aforementioned Calabi–Yau threefold. The dual field theory to this set up has been discussed in the literature, but only in the abelian (N = 1) case. The power of the AdS/CFT correspondence allows us to make predictions for N > 1 which are otherwise inaccessible from the field theory side with current technology. We compute the holographic central charges and show that these agree with the field theory and with the anomalies of self-dual strings in 6d. We complement our analysis with a discussion of the dual M-theory solutions and a comparison of the central charges. We supplement our (0, 4) analysis with a discussion on (0, 2) solutions. We discuss three classes of solutions with varying axio-dilaton. It is interesting to note that contrary to the popular F-theory lore, Ricci-flat (i.e. Calabi–Yau) manifolds are not a necessary condition for an F-theory geometry. In each of these classes we compare the holographic central charges with field theory results obtained by using c-extremisation, finding perfect agreement. In the final chapter of this thesis we complete the classification of AdS5 solutions in Type IIB by extending the existing classification to allow for vanishing self-dual five-form. AdS5 solutions with vanishing five-form have been found recently which evaded the previous classification and we show how these solutions fit into the ex-tended classification presented here. We allow throughout for a varying axio-dilaton.

Date of Award	2019
Original language	English
Awarding Institution	King's College London
Supervisor	Dario Martelli (Supervisor) & Peter West (Supervisor)