Gravitational F-terms of SO/Sp gauge theories and anomalies

Abstract

We study the first non trivial gravitational corrections to the F-terms of ${\cal N}=1$ SYM SO/Sp gauge theories, with matter in some representations, by using the generalized Konishi anomaly method. We derive equations at genus one for the operators in the chiral ring and compare them with the loop equations of the corresponding matrix models, finding agreement. We find that for adjoint representation the genus 0 contributions to such corrections can be adsorbed by a field redefinition; remarkably, this is not the case for matter in the (anti-)symmetric representation of ($Sp$) $SO$.