Instantons on Calabi-Yau and hyper-Kähler cones

Jakob C. Geipel; Marcus Sperling

doi:10.1007/JHEP10(2017)103

Instantons on Calabi-Yau and hyper-Kähler cones

Jakob C. Geipel (Corresponding author)
, Marcus Sperling

Mathematical Physics

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

The instanton equations on vector bundles over Calabi-Yau and hyper-Kähler cones can be reduced to matrix equations resembling Nahm’s equations. We complement the discussion of Hermitian Yang-Mills (HYM) equations on Calabi-Yau cones, based on regular semi-simple elements, by a new set of (singular) boundary conditions which have a known instanton solution in one direction. This approach extends the classic results of Kronheimer by probing a relation between generalised Nahm’s equations and nilpotent pairs/tuples. Moreover, we consider quaternionic instantons on hyper-Kähler cones over generic 3-Sasakian manifolds and study the HYM moduli spaces arising in this set-up, using the fact that their analysis can be traced back to the intersection of three Hermitian Yang-Mills conditions.

Original language	English
Article number	103
Number of pages	33
Journal	Journal of High Energy Physics
Volume	2017
Issue number	10
DOIs	https://doi.org/10.1007/JHEP10(2017)103
Publication status	Published - 16 Oct 2017

Funding

We are grateful to Fabio Apruzzi, Felix Lubbe, Alexander D. Popov, and Markus Miser for valuable discussions and comments. This work was done within the framework of the DFG project LE 838/13. JG is supported by the DFG research training group GRK1463 "Analysis, Geometry, and String Theory". MS is supported by Austrian Science Fund (FWF) grant P28590.

Austrian Fields of Science 2012

103012 High energy physics
101006 Differential geometry

Keywords

Solitons Monopoles and Instantons
Differential and Algebraic Geometry
Gauge Symmetry
PRINCIPAL NILPOTENT PAIRS
SEMISIMPLE LIE-ALGEBRAS
NAHMS EQUATIONS
VECTOR-BUNDLES
CLASSIFICATION
CONNECTIONS
DIMENSIONS
MANIFOLDS
TOPOLOGY
GEOMETRY

Access to Document

10.1007/JHEP10(2017)103Licence: CC BY 4.0

http://phaidra.univie.ac.at/o:877089Licence: CC BY 4.0

Cite this

@article{564311f1f4db450b806e2d8d1dc763bd,

title = "Instantons on Calabi-Yau and hyper-K{\"a}hler cones",

abstract = "The instanton equations on vector bundles over Calabi-Yau and hyper-K{\"a}hler cones can be reduced to matrix equations resembling Nahm{\textquoteright}s equations. We complement the discussion of Hermitian Yang-Mills (HYM) equations on Calabi-Yau cones, based on regular semi-simple elements, by a new set of (singular) boundary conditions which have a known instanton solution in one direction. This approach extends the classic results of Kronheimer by probing a relation between generalised Nahm{\textquoteright}s equations and nilpotent pairs/tuples. Moreover, we consider quaternionic instantons on hyper-K{\"a}hler cones over generic 3-Sasakian manifolds and study the HYM moduli spaces arising in this set-up, using the fact that their analysis can be traced back to the intersection of three Hermitian Yang-Mills conditions.",

keywords = "Solitons Monopoles and Instantons, Differential and Algebraic Geometry, Gauge Symmetry, PRINCIPAL NILPOTENT PAIRS, SEMISIMPLE LIE-ALGEBRAS, NAHMS EQUATIONS, VECTOR-BUNDLES, CLASSIFICATION, CONNECTIONS, DIMENSIONS, MANIFOLDS, TOPOLOGY, GEOMETRY",

author = "Geipel, \{Jakob C.\} and Marcus Sperling",

note = "Publisher Copyright: {\textcopyright} 2017, The Author(s).",

year = "2017",

month = oct,

day = "16",

doi = "10.1007/JHEP10(2017)103",

language = "English",

volume = "2017",

journal = "Journal of High Energy Physics",

issn = "1029-8479",

publisher = "Springer",

number = "10",

}

TY - JOUR

T1 - Instantons on Calabi-Yau and hyper-Kähler cones

AU - Geipel, Jakob C.

AU - Sperling, Marcus

PY - 2017/10/16

Y1 - 2017/10/16

N2 - The instanton equations on vector bundles over Calabi-Yau and hyper-Kähler cones can be reduced to matrix equations resembling Nahm’s equations. We complement the discussion of Hermitian Yang-Mills (HYM) equations on Calabi-Yau cones, based on regular semi-simple elements, by a new set of (singular) boundary conditions which have a known instanton solution in one direction. This approach extends the classic results of Kronheimer by probing a relation between generalised Nahm’s equations and nilpotent pairs/tuples. Moreover, we consider quaternionic instantons on hyper-Kähler cones over generic 3-Sasakian manifolds and study the HYM moduli spaces arising in this set-up, using the fact that their analysis can be traced back to the intersection of three Hermitian Yang-Mills conditions.

AB - The instanton equations on vector bundles over Calabi-Yau and hyper-Kähler cones can be reduced to matrix equations resembling Nahm’s equations. We complement the discussion of Hermitian Yang-Mills (HYM) equations on Calabi-Yau cones, based on regular semi-simple elements, by a new set of (singular) boundary conditions which have a known instanton solution in one direction. This approach extends the classic results of Kronheimer by probing a relation between generalised Nahm’s equations and nilpotent pairs/tuples. Moreover, we consider quaternionic instantons on hyper-Kähler cones over generic 3-Sasakian manifolds and study the HYM moduli spaces arising in this set-up, using the fact that their analysis can be traced back to the intersection of three Hermitian Yang-Mills conditions.

KW - Solitons Monopoles and Instantons

KW - Differential and Algebraic Geometry

KW - Gauge Symmetry

KW - PRINCIPAL NILPOTENT PAIRS

KW - SEMISIMPLE LIE-ALGEBRAS

KW - NAHMS EQUATIONS

KW - VECTOR-BUNDLES

KW - CLASSIFICATION

KW - CONNECTIONS

KW - DIMENSIONS

KW - MANIFOLDS

KW - TOPOLOGY

KW - GEOMETRY

UR - https://www.scopus.com/pages/publications/85032023601

U2 - 10.1007/JHEP10(2017)103

DO - 10.1007/JHEP10(2017)103

M3 - Article

SN - 1029-8479

VL - 2017

JO - Journal of High Energy Physics

JF - Journal of High Energy Physics

IS - 10

M1 - 103

ER -

Instantons on Calabi-Yau and hyper-Kähler cones

Abstract

Funding

Austrian Fields of Science 2012

Keywords

Access to Document

Other files and links

Fingerprint

Cite this