Supersymmetry and localization

Schwarz, Albert; Zaboronsky, Oleg

doi:10.1007/bf02506415

Cited by 57 publications

(82 citation statements)

References 13 publications

(23 reference statements)

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“…See also [39,40] for details regarding the localization argument. Starting point for the construction by Qiu and Zabzine is the S 5 theory of [26].…”

Section: The Super Yang-mills Theoriesmentioning

confidence: 99%

Localisation on Sasaki-Einstein manifolds from holomorphic functions on the cone

Schmude

2015

J. High Energ. Phys.

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Abstract:We study super Yang-Mills theories on five-dimensional Sasaki-Einstein manifolds. Using localisation techniques, we find that the contribution from the vector multiplet to the perturbative partition function can be calculated by counting holomorphic functions on the associated Calabi-Yau cone. This observation allows us to use standard techniques developed in the context of quiver gauge theories to obtain explicit results for a number of examples; namely S 5 ,

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“…See also [39,40] for details regarding the localization argument. Starting point for the construction by Qiu and Zabzine is the S 5 theory of [26].…”

Section: The Super Yang-mills Theoriesmentioning

confidence: 99%

Localisation on Sasaki-Einstein manifolds from holomorphic functions on the cone

Schmude

2015

J. High Energ. Phys.

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“…Using these variables, the partition function can be written in a completely "linearized" form: 15) where the action is…”

Section: The Instanton Calculus and Localizationmentioning

confidence: 99%

“…Since the result is independent of s, under favourable circumstances-which will be shown to hold in the present application-the Gaussian approximation is exact (for references to this kind of localization in the physics literature see Refs. [12][13][14][15] and references therein). In the present case, the presence of an effective action for instantons arises from the fact that instanton are constrained on the Coulomb branch.…”

Section: Introductionmentioning

confidence: 99%

Calculating the prepotential by localization on the moduli space of instantons

Hollowood¹

2002

J. High Energy Phys.

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We describe a new technique for calculating instanton effects in supersymmetric gauge theories applicable on the Higgs or Coulomb branches. In these situations the instantons are constrained and a potential is generated on the instanton moduli space. Due to existence of a nilpotent fermionic symmetry the resulting integral over the instanton moduli space localizes on the critical points of the potential. Using this technology we calculate the one-and two-instanton contributions to the prepotential of SU(N) gauge theory with N = 2 supersymmetry and show how the localization approach yields the prediction extracted from the Seiberg-Witten curve. The technique appears to extend to arbitrary instanton number in a tractable way.

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Section: )mentioning

confidence: 99%

Testing Seiberg–Witten theory to all orders in the instanton expansion

Hollowood

2002

Nuclear Physics B

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In the context of softly-broken N = 4 to N = 2 supersymmetric SU(N) gauge theory, we calculate using semi-classical instanton methods, the lowest order non-trivial terms in the mass expansion of the prepotential for all instanton number. We find exact agreement with Seiberg-Witten theory and thereby achieve the most powerful test yet of this theory. We also calculate the one-and two-instanton contributions completely and also find consistency with Seiberg-Witten theory. Our approach relies on the fact that the instanton calculus admits a nilpotent fermionic symmetry, or BRST operator, whose existence implies that the integrals over the instanton moduli space, which give the coefficients of the prepotential, localize on the space of resolved point-like instantons or what we call "topicons".

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Supersymmetry and localization

Abstract: We study conditions under which an odd symmetry of the integrand leads to localization of the corresponding integral over a (super)manifold. We also show that in many cases these conditions guarantee exactness of the stationary phase approximation of such integrals.Comment: 16 pages, LATE

Cited by 57 publications

References 13 publications

Localisation on Sasaki-Einstein manifolds from holomorphic functions on the cone

Localisation on Sasaki-Einstein manifolds from holomorphic functions on the cone

Calculating the prepotential by localization on the moduli space of instantons

Testing Seiberg–Witten theory to all orders in the instanton expansion

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