Narrow Results

We show that for a large class of conformal field theories the 1/N correction to the chiral anomaly of the U(1) R-current can be shown to arise from the D7-branes present in the dual orientifolded orbifold string theories, generalizing a result in the literature for the simplest case. We also study the U(1)_R anomaly for conformal field theories that arise from orientifolds of the conifold. We find agreement between the field- and string-theoretic calculations, confirming a prediction of the AdS/CFT correspondence at order 1/N for string theories on AdS₅ × T¹¹/ℤ₂.

The membrane instanton superpotential for M-theory on the G₂ holonomy manifold given by the cone on S³×S³ is given by the dilogarithm and has Heisenberg monodromy group in the quantum moduli space. We compare this to a Heisenberg group action on the type IIA hypermultiplet moduli space for the universal hypermultiplet, to metric corrections from membrane instantons related to a twisted dilogarithm for the deformed conifold and to a flat bundle related to a conifold period, the Heisenberg group and the dilogarithm appearing in five-dimensional Seiberg/Witten theory.

Gravity duals for a class of UV complete minimally supersymmetric nonconformal gauge theories require deformed conifolds with fluxes. However these manifolds do not allow for the standard Kähler or conformally Kähler metrics on them, instead the metrics are fully non-Kähler. We take a generic such configuration of a non-Kähler deformed conifold with fluxes and ask what constraints do supersymmetry impose in the baryonic branch. We study the supersymmetry conditions and show that for the correct choices of the vielbeins and the complex structure all the equations may be consistently solved. The constraints now lead not only to the known cases in the literature but also to some new backgrounds. We also show how geometric features of these backgrounds, including the overall warp-factor and the resolution parameters, can be seen on the field theory side from perturbative “probe-brane” type calculations by Higgsing the theory and studying one-loop 4-point functions of vector and chiral multiplets. Finally we discuss how UV completions of these gauge theories may be seen from our setup, both from type IIB as well as from the T-dual type IIA brane constructions.