Instantons at strong coupling, averaging over vacua, and the gluino condensate

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We consider instanton contributions to chiral correlators, such as <0|Tr λ2(x)Tr λ2(x′)|0>, in script 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 script N = 1 vacuum. We observe a numerical discrepancy, coinciding with that observed previously in script N = 1 SQCD. Moreover, since knowledge of the vacuum structure is complete for softly broken script N = 2 Yang-Mills, this model serves as a counter example to the hypothesis of Amati et al. that 1-instanton calculations at strong coupling can be interpreted as averaging over vacua. Within script 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 non-zero value through infra-red effects when calculated in the unbroken phase.

Original languageEnglish (US)
Pages (from-to)311-328
Number of pages18
JournalNuclear Physics B
Issue number1-2
StatePublished - Jan 31 2000

Bibliographical note

Funding Information:
We would like to thank A. Gorsky, I. Kogan, A. Kovner, M. Shifman, and A. Yung for helpful discussions. This work was supported in part by the Department of Energy under Grant No. DE-FG02-94ER40823.


  • Instantons
  • Supersymmetric gauge theory


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