G2–instantons Over Asymptotically Cylindrical Manifolds

@article{Earp2011G2instantonsOA,
  title={G2–instantons Over Asymptotically Cylindrical Manifolds},
  author={Henrique N. S{\'a} Earp},
  journal={Scopus},
  year={2011}
}
  • H. S. Earp
  • Published 5 January 2011
  • Mathematics
  • Scopus
A concrete model for a 7-dimensional gauge theory under special holonomy is proposed, within the paradigm outlined by Donaldson and Thomas, over the asymptotically cylindrical G2-manifolds provided by Kovalev's noncompact version of the Calabi conjecture. One obtains a solution to the $G_2$-instanton equation from the associated Hermitian Yang-Mills problem, to which the methods of Simpson et al. are applied, subject to a crucial asymptotic stability assumption over the "boundary at infinity". 

Figures from this paper

Deformations of Nearly Kähler Instantons

We formulate the deformation theory for instantons on nearly Kähler six-manifolds using spinors and Dirac operators. Using this framework we identify the space of deformations of an irreducible

Generalised Chern-Simons Theory and G2-Instantons over Associative Fibrations

Adjusting conventional Chern{Simons theory to G2-manifolds, one describes G2-instantons on bundles over a certain class of 7-dimensional flat tori which fiber non- trivially over T 4 , by a pullback

Holomorphic bundles for higher dimensional gauge theory

Motivated by gauge theory under special holonomy, we present techniques to produce holomorphic bundles over certain non‐compact 3‐folds, called building blocks, satisfying a stability condition ‘at

Explicit abelian instantons on $S^1$-invariant K\"ahler Einstein $6$-manifolds

. We consider a dimensional reduction of the Hermitian Yang-Mills condition on S 1 -invariant Kähler Einstein 6 -manifolds. This allows us to re-formulate the Hermitian Yang-Mills equations in terms

G2-instantons over twisted connected sums

We introduce a method to construct G2 ‐instantons over compact G2 ‐manifolds arising as the twisted connected sum of a matching pair of building blocks. Our construction is based on gluing G2

Marginal deformations of heterotic G2 sigma models

A bstractRecently, the infinitesimal moduli space of heterotic G2 compactifications was described in supergravity and related to the cohomology of a target space differential. In this paper we

Construction of G 2 -instantons via twisted connected sums

We propose a method to construct G_2-instantons over a compact twisted connected sum G_2-manifold, applying a gluing result of S\'a Earp and Walpuski to instantons over a pair of 7-manifolds with a

Hermitian Yang–Mills metrics on reflexive sheaves over asymptotically cylindrical Kähler manifolds

Abstract We prove an analogue of the Donaldson–Uhlenbeck–Yau theorem for asymptotically cylindrical (ACyl) Kähler manifolds: If is a reflexive sheaf over an ACyl Kähler manifold, which is asymptotic

Asymptotic behaviour of $Spin(7)$-instantons on Cylinder Manifolds

In this article,we study the asymptotic behaviour of $Spin(7)$-instantons with square integrable curvature on the cylindrical over a compact $G_{2}$-manifold has fully holomony.We can prove that the

G2-instantons on generalised Kummer constructions

In this article we introduce a method to construct $\rm{G}_2$-instantons on $\rm{G}_2$-manifolds arising from Joyce's generalised Kummer construction. The method is based on gluing ASD instantons

References

SHOWING 1-10 OF 45 REFERENCES

G 2 − instantons over Kovalev manifolds I

A concrete model for a 7-dimensional gauge theory under special holonomy is proposed, within the paradigm of Donaldson and Thomas [D-T], over the asymptotically cylindrical G2−manifolds provided by

G2-instantons on generalised Kummer constructions

In this article we introduce a method to construct $\rm{G}_2$-instantons on $\rm{G}_2$-manifolds arising from Joyce's generalised Kummer construction. The method is based on gluing ASD instantons

Twisted connected sums and special Riemannian holonomy

We give a new, connected-sum-like construction of Riemannian metrics with special holonomy G_2 on compact 7-manifolds. The construction is based on a gluing theorem for appropriate elliptic partial

to complex geometry

We construct from a real ane manifold with singularities (a tropical manifold) a degeneration of Calabi-Yau manifolds. This solves a fundamental problem in mirror symmetry. Furthermore, a striking

G2 geometry and integrable systems

We study the Hitchin component in the space of representations of the fundamental group of a Riemann surface into a split real Lie group in the rank 2 case. We prove that such representations are

Gauge theory and calibrated geometry, I

The geometry of submanifolds is intimately related to the theory of functions and vector bundles. It has been of fundamental importance to find out how those two objects interact in many geometric

Gauge theory on Calabi-Yau manifolds

We study complex analogues on Calabi-Yau manifolds of gauge theories on low dimensional real manifolds. In particular we define a holomorphic analogue of the Casson invariant, counting coherent

Instantons and Four-Manifolds

This volume has been designed to explore the confluence of techniques and ideas from mathematical physics and the topological study of the differentiable structure of compact four-dimensional

Compact Manifolds with Special Holonomy

The book starts with a thorough introduction to connections and holonomy groups, and to Riemannian, complex and Kahler geometry. Then the Calabi conjecture is proved and used to deduce the existence