# 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} }

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".

## 32 Citations

### Deformations of Nearly Kähler Instantons

- Mathematics
- 2016

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

- Mathematics
- 2014

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

- Mathematics
- 2011

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

- Mathematics
- 2022

. 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

- Mathematics
- 2013

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

- Mathematics
- 2017

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

- Mathematics
- 2015

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

- MathematicsCommunications in Partial Differential Equations
- 2018

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

- Mathematics
- 2018

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

- Mathematics
- 2011

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

- Mathematics
- 2013

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

- Mathematics
- 2011

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

- Mathematics
- 2000

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

- Mathematics
- 2011

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

- Mathematics
- 2009

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

- Mathematics
- 2000

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

- Mathematics
- 1997

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

- Mathematics
- 1984

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

- Mathematics
- 2000

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…