Konishi anomaly approach to gravitational F-terms

We study gravitational corrections to the effective superpotential in theories with a single adjoint chiral multiplet, using the generalized Konishi anomaly and the gravitationally deformed chiral ring. We show that the genus one correction to the loop equation in the corresponding matrix model agrees with the gravitational corrected anomaly equations in the gauge theory. An important ingrediant in the proof is the lack of factorization of chiral gauge invariant operators in presence of a supergravity background. We also find a genus zero gravitational correction to the superpotential, which can be removed by a field redefinition.