English

# Item

ITEM ACTIONSEXPORT
Instantons on hyperkähler manifolds

Devchand, C., Pontecorvo, M., & Spiro, A. (in preparation). Instantons on hyperkähler manifolds.

Item is

show hide
Genre: Paper

### Files

show Files
hide Files
:
1812.06498.pdf (Preprint), 435KB
Name:
1812.06498.pdf
Description:
Visibility:
Public
MIME-Type / Checksum:
application/pdf / [MD5]
-
-

show

### Creators

show
hide
Creators:
Devchand, Chandrashekar1, Author
Pontecorvo, Massimiliano, Author
Spiro, Andrea, Author
Affiliations:
1Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society, ou_24014

### Content

show
hide
Free keywords: Mathematics, Differential Geometry, math.DG,High Energy Physics - Theory, hep-th,Mathematical Physics, math-ph,Mathematics, Mathematical Physics, math.MP,
Abstract: An instanton $(E, D)$ on a (pseudo-)hyperk\"ahler manifold $M$ is a vector bundle $E$ associated to a principal $G$-bundle with a connection $D$ whose curvature is pointwise invariant under the quaternionic structures of $T_x M, \ x\in M$, and thus satisfies the Yang-Mills equations. Revisiting a construction of solutions, we prove a local bijection between gauge equivalence classes of instantons on $M$ and equivalence classes of certain holomorphic functions taking values in the Lie algebra of $G^\mathbb{C}$ defined on an appropriate $SL_2(\mathbb{C})$-bundle over $M$. Our reformulation affords a streamlined proof of Uhlenbeck's Compactness Theorem for instantons on (pseudo-)hyperk\"ahler manifolds.

### Details

show
hide
Language(s):
Dates: 2018-12-16
Publication Status: Not specified
Pages: 35 pages
Publishing info: -
Rev. Method: -
Identifiers: arXiv: 1812.06498
URI: http://arxiv.org/abs/1812.06498
Degree: -

show

show

show

show