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

TL;DR

This paper investigates gravitational corrections to the F-terms in ${\

Contribution

It introduces a method to compute genus one gravitational corrections in SO/Sp gauge theories using generalized Konishi anomalies, revealing representation-dependent effects.

Findings

Genus one corrections match matrix model loop equations.

Field redefinition absorbs genus zero corrections for adjoint matter.

Matter in (anti-)symmetric representations exhibits non-absorbable corrections.

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 ($Sp$) $SO$.