Supersymmetry transformations of instantons

Novikov, V.A.; Shifman, M.; Vainshtein, A.I.; Voloshin, V. B.; Захаров, В. И.

doi:10.1016/0550-3213(83)90339-5

Cited by 263 publications

(412 citation statements)

References 8 publications

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“…In the first methodology [8][9][10]-and in the present context the "suspect" method, because it involves a semi-classical analysis directly in the strongly-coupled confining phase of the gauge theory-the so-called strong-coupling instanton (SCI) approach, the gluino condensate trλ 2 is determined via an explicit one-instanton calculation of a certain multipoint function of tr λ 2 . Cluster decomposition arguments are then invoked in order to extract the one-point function trλ 2 .…”

Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

Monopoles, affine algebras and the gluino condensate

Davies

Hollowood

Khoze

2003

Journal of Mathematical Physics

131

306

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We examine the low-energy dynamics of four-dimensional supersymmetric gauge theories and calculate the values of the gluino condensate for all simple gauge groups. By initially compactifying the theory on a cylinder we are able to perform calculations in a controlled weakly-coupled way for small radius. The dominant contributions to the path integral on the cylinder arise from magnetic monopoles which play the role of instanton constituents. We find that the semi-classically generated superpotential of the theory is the affine Toda potential for an associated twisted affine algebra. We determine the supersymmetric vacua and calculate the values of the gluino condensate. The number of supersymmetric vacua is equal to c 2 , the dual Coxeter number, and in each vacuum the monopoles carry a fraction 1/c 2 of topological charge. As the results are independent of the radius of the circle, they are also valid in the strong coupling regime where the theory becomes decompactified. In this way we obtain values for the gluino condensate which for the classical gauge groups agree with previously known "weak coupling instanton" expressions (but not with the "strong coupling instanton" calculations). This detailed agreement provides further evidence in favour of the recently advocated resolution of the the gluino condensate puzzle. We also make explicit predictions for the gluino condensate for the exceptional groups.

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Section: Introduction and Summary Of Resultsmentioning

confidence: 99%

Monopoles, affine algebras and the gluino condensate

Davies

Hollowood

Khoze

2003

Journal of Mathematical Physics

131

306

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“…Given certain topological conditions on Σ 4 , discussed further belowheuristically, one asks that Σ 4 have no deformations that could correspond to charged matter fields -the four-dimensional gauge theory arising upon dimensional reduction is pure glue N = 1 super Yang-Mills theory. At low energies, this field theory generates a nonperturbative superpotential from gaugino condensation [328][329][330][331][332][333] (cf. [334]):…”

Section: Nonperturbative Effectsmentioning

confidence: 99%

Inflation and String Theory

2015

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“…Historically, the first arena in which supersymmetry and nonperturbative instanton effects were successfully integrated was in the direct calculation of certain chiral correlators [1]. These correlators involve the lowest components of chiral superfields, and a well-known example in N = 1 supersymmetric Yang-Mills (SYM) with gauge group SU(2) is the 2-point function of gluino bilinears 0|Tr λ 2 (x) Tr λ 2 (x ′ )|0 .…”

Section: Introductionmentioning

confidence: 99%

“…During the eighties, two different techniques for instanton calculations in this context were developed. The "strong-coupling instanton" (SCI) approach [1,4,5,6] (see [7] for a review), applies in strongly coupled theories such as N = 1 SYM where the instanton is an exact solution to the equations of motion, and involves a direct integration over the instanton zero modes. For a given correlator, only a given instanton order can contribute, and the integration over instanton size ρ is peaked at ρ ∼ |x − x ′ |.…”

Section: Introductionmentioning

confidence: 99%

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

Ritz

Vainshtein

2000

Nuclear Physics B

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We consider instanton contributions to chiral correlators, such as 0|Trλ 2 (x)Trλ 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 YangMills, 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.

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Supersymmetry transformations of instantons

Cited by 263 publications

References 8 publications

Monopoles, affine algebras and the gluino condensate

Monopoles, affine algebras and the gluino condensate

Inflation and String Theory

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

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