On Nonperturbative Exactness of Konishi Anomaly and the Dijkgraaf-Vafa Conjecture

TL;DR

This paper demonstrates that the generalized Konishi anomaly remains nonperturbatively exact in certain supersymmetric gauge theories, supporting the Dijkgraaf-Vafa conjecture by analyzing algebraic structures and superpotential corrections.

Contribution

It proves the nonperturbative exactness of the Konishi anomaly algebra in specific gauge theories and discusses implications for the Dijkgraaf-Vafa conjecture.

Findings

The algebra of chiral rotations does not receive nonperturbative corrections.

Superpotentials of degree less than 2l+1 are not nonperturbatively renormalized.

Higher degree superpotentials can be renormalized due to UV ambiguities.

Abstract

In this paper we study the nonperturbative corrections to the generalized Konishi anomaly that come from the strong coupling dynamics of the gauge theory. We consider U(N) gauge theory with adjoint and Sp(N) or SO(N) gauge theory with symmetric or antisymmetric tensor. We study the algebra of chiral rotations of the matter field and show that it does not receive nonperturbative corrections. The algebra implies Wess-Zumino consistency conditions for the generalized Konishi anomaly which are used to show that the anomaly does not receive nonperturbative corrections for superpotentials of degree less than 2l+1 where 2l=3c(Adj)-c(R) is the one-loop beta function coefficient. The superpotentials of higher degree can be nonperturbatively renormalized because of the ambiguities in the UV completion of the gauge theory. We discuss the implications for the Dijkgraaf-Vafa conjecture.