$R$-Symmetries, Algebraic Geometry, and AdS/CFT

We study the flow of central charges in $N= 1$ supersymmetric gauge theories which admit large TV supergravity duals. For theories lying in the conformal window, supersymmetry relates this evolution to a renormalization of the $R$-charges, and this information can, in many cases, be extracted from the dual geometry making use of the conserved U(1)s current along the flow. In particular, we argue that these charges are determined purely by the complex structure of the 6-dimensional manifold transverse to the D-branes which source the geometry. We demonstrate this relationship in a class of flows between $A_k$ orbifolds and generalized conifolds.