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The complex dimension of the space of exactly marginal deformations forquiver CFTs dual to IIB theory compactified on $Y^{p,q}$ is known to begenerically three. Simple general formulas already exist for two of the exactlymarginal directions in the space of couplings, one of which corresponds to thesum of the (inverse squared of) gauge couplings, and the other to the$\beta$-deformation. Here we identify the third exactly marginal direction,which is dual to the modulus $\int B_{2}$ on the gravity side. Thisidentification leads to a relation between the field theory gauge couplings andthe vacuum expectation value of the gravity modulus that we further support bya computation related to the chiral anomaly induced by added fractional branes.We also present a simple algorithm for finding similar exactly marginaldirections in any CFT described by brane tiling, and demonstrate it for thequiver CFTs dual to IIB theory compactified on $L^{1,5,2}$ and the SuspendedPinch Point.

On Exactly Marginal Deformations Dual to $B$-Field Moduli of IIB Theory on SE$_5$