Hyperkähler quotients and algebraic curves

Ulf Lindström; Martin Roček; Rikard Von Unge

Hyperkähler quotients and algebraic curves

Ulf Lindström
, Martin Roček
, Rikard Von Unge

Institute for Theoretical Physics

Stockholm University
Masaryk University

Research output: Contribution to journal › Article › peer-review

23 Scopus citations

Abstract

We develop a graphical representation of polynomial invariants of unitary gauge groups, and use it to find the algebraic curve corresponding to a hyperkähler quotient of a linear space. We apply this method to four dimensional ALE spaces, and for the A_k, D_k, and E₆ cases, derive the explicit relation between the deformations of the curves away from the orbifold limit and the Fayet-Iliopoulos parameters in the corresponding quotient construction. We work out the orbifold limit of E₇, E₈, and some higher dimensional examples.

Original language	English
Article number	022
Journal	Journal of High Energy Physics
Volume	4
Issue number	1
State	Published - 2000

Keywords

Differential and Algebraic Geometry
Sigma Models
Superstring Vacua
Supersymmetric Effective Theories

Cite this

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title = "Hyperk{\"a}hler quotients and algebraic curves",

abstract = "We develop a graphical representation of polynomial invariants of unitary gauge groups, and use it to find the algebraic curve corresponding to a hyperk{\"a}hler quotient of a linear space. We apply this method to four dimensional ALE spaces, and for the Ak, Dk, and E6 cases, derive the explicit relation between the deformations of the curves away from the orbifold limit and the Fayet-Iliopoulos parameters in the corresponding quotient construction. We work out the orbifold limit of E7, E8, and some higher dimensional examples.",

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AU - Von Unge, Rikard

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AB - We develop a graphical representation of polynomial invariants of unitary gauge groups, and use it to find the algebraic curve corresponding to a hyperkähler quotient of a linear space. We apply this method to four dimensional ALE spaces, and for the Ak, Dk, and E6 cases, derive the explicit relation between the deformations of the curves away from the orbifold limit and the Fayet-Iliopoulos parameters in the corresponding quotient construction. We work out the orbifold limit of E7, E8, and some higher dimensional examples.

KW - Differential and Algebraic Geometry

KW - Sigma Models

KW - Superstring Vacua

KW - Supersymmetric Effective Theories

UR - https://www.scopus.com/pages/publications/7444251789

M3 - Article

AN - SCOPUS:7444251789

SN - 1126-6708

VL - 4

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 1

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ER -

Hyperkähler quotients and algebraic curves

Abstract

Keywords

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