arXiv research

We consider Lie(G)-valued G-invariant connections on bundles over spaces G/H, RxG/H and R^2xG/H, where G/H is a compact nearly Kaehler six-dimensional homogeneous space, and the manifolds RxG/H and R^2xG/H carry G_2- and Spin(7)-structures, respectively. By making a G-invariant ansatz, Yang-Mills theory with torsion on…

We consider cones over manifolds admitting real Killing spinors and instanton equations on connections on vector bundles over these manifolds. Such cones are manifolds with special (reduced) holonomy. We generalize the scalar ansatz for a connection proposed by Harland and Nolle in such a way that instantons are parame…

5D SCFTs can have confining vacua with strings and unbroken symmetries.

The existence of K-instantons on a cylinder M^7 = R_tau x K/H over a homogeneous nearly K"ahler 6-manifold K/H requires a conformally parallel or a cocalibrated G_2-structure on M^7. The generalized anti-self-duality on M^7 implies a Chern-Simons flow on K/H which runs between instantons on the coset. For K-equivariant…

We study the physics of globally consistent four-dimensional $\mathcal{N}=1$ supersymmetric M-theory compactifications on $G_2$ manifolds constructed via twisted connected sum; there are now perhaps fifty million examples of these manifolds. We study a rich example that exhibits $U(1)^3$ gauge symmetry and a spectrum o…

We study the integrability of the conformal geodesic flow (also known as the conformal circle flow) on the $SO(3)$--invariant gravitational instantons. On a hyper--Kähler four--manifold the conformal geodesic equations reduce to geodesic equations of a charged particle moving in a constant self--dual magnetic field. In…

Classifies gravitational instantons with quadratic volume growth.

Given two hyperkähler manifolds $M$ and $N$ and a quaternionic instanton on their product, a hyperkähler Nahm transform can be defined, which maps quaternionic instantons on $M$ to quaternionic instantons on $N$. This construction includes the case of Nahm transform for periodic instantons on $\bR^4$, the Fourier-Mukai…

Study calculates ring structure in instanton homology for a surface with points.

Survey of recent progress in gravitational instantons

Study shows instantons and monopoles decompose into U(1) components.

We construct a spectral sequence from the reduced odd Khovanov homology of a link converging to the framed instanton homology of the double cover branched over the link, with orientation reversed. Framed instanton homology counts certain instantons on the cylinder of a 3-manifold connect-summed with a 3-torus. En route…

Sp(n)-instantons linked to complex Lagrangian graphs via Fourier-Mukai transform.

Study on Yang-Mills equation near instanton-anti-instanton configurations with energy constraints.

Proves exact triangle linking knot instanton Floer homology to surgeries.

The paper proves unique characterization of gravitational instantons with specific volume growth.

We study the deformation theory of $\mathrm{G}_2$-instantons on the 7-sphere, specifically those obtained from instantons on the 4-sphere via the quaternionic Hopf fibration. We find that the pullback of the standard ASD instanton lies in a smooth, complete, 15-dimensional family of $\mathrm{G}_2$-instantons. In genera…

Proves unique ALE instanton with toric Hermitian structure.

Classifies instantons on a specific gravitational instanton and computes partition functions.

We investigate instantons on manifolds with Killing spinors and their cones. Examples of manifolds with Killing spinors include nearly Kaehler 6-manifolds, nearly parallel G_2-manifolds in dimension 7, Sasaki-Einstein manifolds, and 3-Sasakian manifolds. We construct a connection on the tangent bundle over these manifo…

Period maps surjective for certain gravitational instantons.

We consider the Hermitian Yang-Mills (instanton) equations for connections on vector bundles over a 2n-dimensional Kähler manifold X which is a product Y x Z of p- and q-dimensional Riemannian manifold Y and Z with p+q=2n. We show that in the adiabatic limit, when the metric in the Z direction is scaled down, the gauge…

Gravitational instantons are non-Kähler, providing a counterexample to Euclidean Black Hole Uniqueness.

New homological action on sutured instanton homology defined.

Smooth family of G2-instantons over a Kummer construction.

Proves uniqueness of certain $S^1$-symmetric gravitational instantons.

First non-trivial examples of deformed G_2-instantons, distinguishing nearly parallel G_2-structures.

Instantons on multi-Taub-NUT spaces are mapped to bow representations.

In this paper we explicitly calculate the analogue of the 't Hooft SU(2) Yang--Mills instantons on Gibbons--Hawking multi-centered gravitational instantons which come in two parallel families: the multi-Eguchi--Hanson, or A_k ALE gravitational instantons and the multi-Taub--NUT, or A_k ALF gravitational instantons. We …

Explains a 1978 construction for Yang-Mills instantons.

Existence proved for specific types of gravitational instantons.

New $Spin(7)$-instantons constructed on Joyce's manifold.

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 instanton with semisimple structure group with the kernel of an elliptic operator, and prove that abelian instantons are rigid…

Study calculates instanton Floer homology for surgeries on L-space knots.

Derive K-theoretic Donaldson invariants for various 4-manifolds using path integrals and topological twists.

Study on instantons in $G_2$ and $Spin(7)$ manifolds.

Authors prove Torelli theorem for a specific type of gravitational instantons.

Sutured instanton homology uses Heegaard diagrams to bound homology dimensions.

Computes upper bounds for instanton knot homology.

Yang-Mills instantons on ALE gravitational instantons were constructed by Kronheimer and Nakajima in terms of matrices satisfying algebraic equations. These were conveniently organized into a quiver. We construct generic Yang-Mills instantons on ALF gravitational instantons. Our data are formulated in terms of matrix-v…

Defines cobordism maps connecting Khovanov and instanton homologies.

Constructs non-abelian G2-instantons on ALC members of B7 family.

The abstract discusses instantons on flat spaces and provides explicit constructions.

New instantons show Einstein-Maxwell fields are more complex.

Study instanton metrics via Taub-NUT deformations.

This is our third paper in a series on the gravitational instantons. In this paper, we classify ALG and ALH gravitational instantons. In ALG case, we extend Hein's construction slightly and show that it's the only ALG gravitational instanton. In ALH case, we prove a Torelli-type theorem.

Proves infinitesimal rigidity of Hermitian gravitational instantons.

Study G2-instantons on specific Lie groups, finding conditions and structures.