Instantons at Strong Coupling, Averaging over Vacua, and the Gluino Condensate

TL;DR

This paper investigates instanton effects on chiral correlators in N=1 supersymmetric Yang-Mills theory, revealing discrepancies with expectations from Seiberg-Witten solutions and challenging the idea that strong coupling instanton calculations average over vacua.

Contribution

It provides a counterexample to the hypothesis that 1-instanton strong coupling calculations can be interpreted as vacuum averaging, using models with known vacuum structures.

Findings

Discrepancy between instanton calculations and Seiberg-Witten predictions.

Counterexample to instanton averaging hypothesis.

Vanishing of correlator contributions in the Higgs phase.

Abstract

We consider instanton contributions to chiral correlators, such as <0| Tr \lambda^2 (x) Tr \lambda^2(x') |0>, in N=1 supersymmetric Yang-Mills theory with either light adjoint or fundamental matter. Within the former model, extraction of the gluino condensate from a connected 1-instanton diagram, evaluated at strong coupling, can be contrasted with expectations from the Seiberg-Witten solution perturbed to an N=1 vacuum. We observe a numerical discrepancy, coinciding with that observed previously in N=1 SQCD. Moreover, since knowledge of the vacuum structure is complete for softly broken N=2 Yang-Mills, this model serves as a counterexample to the hypothesis of Amati et al. that 1-instanton calculations at strong coupling can be interpreted as averaging over vacua. Within N=1 SQCD, we point out that the connected contribution to the relevant correlators actually vanishes in the weakly coupled Higgs phase, despite having a nonzero value through infra-red effects when calculated in the unbroken phase.