Hyperkähler metrics and supersymmetry

Hitchin, Nigel; Karlhede, A.; Lindström, Ulf; Roček, Martin

doi:10.1007/bf01214418

Cited by 970 publications

(1,408 citation statements)

References 30 publications

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“…By using this fact, the notion of the hyper-Kähler quotient was first found in physics [3,4] and was later formulated mathematically [5]. (We recommend Ref.…”

Section: Introductionmentioning

confidence: 99%

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SO and USp Kähler and hyper-Kähler quotients and lumps

et al. 2009

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We study non-linear σ models whose target spaces are the Higgs phases of supersymmetric SO and U Sp gauge theories by using the Kähler and hyper-Kähler quotient constructions. We obtain the explicit Kähler potentials and develop an expansion formula to make use of the obtained potentials from which we also calculate the curvatures of the manifolds. The 1/2 BPS lumps in the U (1) × SO and U (1) × U Sp Kähler quotients and their effective descriptions are also studied. In this connection, a general relation between moduli spaces of vortices and lumps is discussed. We find a new singular limit of the lumps with non-vanishing sizes in addition to the ordinary small lump singularity. The former is due to the existence of singular submanifolds in the target spaces.

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“…By using this fact, the notion of the hyper-Kähler quotient was first found in physics [3,4] and was later formulated mathematically [5]. (We recommend Ref.…”

Section: Introductionmentioning

confidence: 99%

“…The Dflatness conditions (3.2), however, are rather difficult to solve. 5 Without taking the Wess-Zumino gauge, we can eliminate the superfield V ′ directly within the superfield formalism by using a trick.…”

Section: The U (N C ) Hyper-kähler Quotientmentioning

confidence: 99%

SO and USp Kähler and hyper-Kähler quotients and lumps

et al. 2009

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“…Here, wα,α = 1, 2, are N × k matrices with elements w uiα and a ′ n , n = 1, 2, 3, 4, are k × k Hermitian matrices. 10 The instanton moduli space M k,N is then obtained as a hyperKähler quotient [28] by the group U(k) acting on the variables as…”

Section: The Instanton Calculus and Localizationmentioning

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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“…Finally we would like to give a comment on a relation between the deformed ADHM constraints and the hyper-Kähler quotient construction [30]. In the ordinary (commutative or noncommutative) gauge theory, the fermionic ADHM constraints ensure that the fermionic moduli are Grassmann-valued symplectic tangent vectors of the bosonic moduli space.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Instantons in Script N = 1/2 super Yang-Mills theory via deformed super ADHM construction

Araki¹,

Takashima²,

Watamura³

2005

J. High Energy Phys.

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We study an extension of the ADHM construction to give deformed anti-self-dual (ASD) instantons in N = 1/2 super Yang-Mills theory with U(n) gauge group. First we extend the exterior algebra on superspace to non(anti)commutative superspace and show that the N = 1/2 super Yang-Mills theory can be reformulated in a geometrical way. By using this exterior algebra, we formulate a non(anti)commutative version of the super ADHM construction and show that the curvature two-form superfields obtained by our construction do satisfy the deformed ASD equations and thus we establish the deformed super ADHM construction. We also show that the known deformed U(2) one instanton solution is obtained by this construction.

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Hyperkähler metrics and supersymmetry

Cited by 970 publications

References 30 publications

SO and USp Kähler and hyper-Kähler quotients and lumps

SO and USp Kähler and hyper-Kähler quotients and lumps

Calculating the prepotential by localization on the moduli space of instantons

Instantons in Script N = 1/2 super Yang-Mills theory via deformed super ADHM construction

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