Related papers: Twistor spaces for hyperkaehler implosions

In this note we prove a new explicit formula for the invariants of moduli spaces of twisted Higgs bundles over P^1 and we relate these invariants to the invariants of moduli spaces of representations of some infinite symmetric quiver. The…

We study the algebraic geometry of twisted Higgs bundles of cyclic type along complex curves. These objects, which generalize ordinary cyclic Higgs bundles, can be identified with representations of a cyclic quiver in a twisted category of…

This thesis was motivated by a desire to understand the natural geometry of hyperbolic monopole moduli spaces. We take two approaches. Firstly we develop the twistor theory of singular hyperbolic monopoles and use it to study the geometry…

The general construction of self-adjoint configuration space representations of the Heisenberg algebra over an arbitrary manifold is considered. All such inequivalent representations are parametrised in terms of the topology classes of flat…

We study a system of equations on a compact complex manifold, that couples the scalar curvature of a Kaehler metric with a spectral function of a first-order deformation of the complex structure. The system comes from an…

Recently, conformal field theories in six dimensions were discussed from the twistorial point of view. In particular, it was demonstrated that the twistor transform between chiral zero-rest-mass fields and cohomology classes on twistor…

We consider a Hamiltonian action of n-dimensional torus, T^n, on a compact symplectic manifold (M,\omega) with d isolated fixed points. For every fixed point p there exists (though not unique) a class a_p in H^*_{T}(M; Q) such that the…

This is a review article exploring similarities between moduli of quiver representations and moduli of vector bundles over a smooth projective curve. After describing the basic properties of these moduli problems and constructions of their…

We study the twisted indices of $\mathcal{N}=4$ supersymmetric gauge theories in three dimensions on spatial $S^{2}$ with an angular momentum refinement. We demonstrate factorisation of the index into holomorphic blocks for the $T[SU(N)]$…

We study aspects of 3d $\mathcal{N}=2$ supersymmetric gauge theories on the product of a line and a Riemann surface. Performing a topological twist along the Riemann surface leads to an effective supersymmetric quantum mechanics on the…

The compact complex manifolds considered in this article are principal torus bundles over a torus. We consider the Kodaira Spencer map of the complete Appell Humbert family (introduced by the first author in Part I) and are able to show…

Multidimensional Heisenberg algebras, whose creation and annihilation operators are the N-dimensional vectors, can be injected into simple Lie algebras g. It is demonstrated that the spectrum of their deformations can be investigated using…

We develop a theory of twistor spaces for supersingular K3 surfaces, extending the analogy between supersingular K3 surfaces and complex analytic K3 surfaces. Our twistor spaces are obtained as relative moduli spaces of twisted sheaves on…

For a very ample line bundle L on a compact connected complex manifold X, with a real structure, we discuss entanglement properties of certain sequences of vectors in tensor products of spaces of holomorphic sections of powers of L.

We compare the invariants of flat vector bundles defined by Atiyah et al. and Jones et al. and prove that, up to weak homotopy, they induce the same map, denoted by $e$, from the $0$-connective algebraic $K$-theory space of the complex…

The generalized Legendre transform method of Lindstrom and Rocek yields hyperkaehler metrics from holomorphic functions. Its main ingredients are sections of ${\cal O}(2j)$ bundles over the twistor space satisfying a reality condition with…

We construct a fully interacting holomorphic/topological theory in eleven dimensions that is defined on products of Calabi-Yau fivefolds with real one-manifolds. The theory describes a particular deformation of the cotangent bundle to the…

We perform the twistor (half-Fourier) transform of all tree n-particle superamplitudes in N=4 SYM and show that it has a transparent geometric interpretation. We find that the N^kMHV amplitude is supported on a set of (2k+1) intersecting…

Motivated by generalized geometry (\`a la Hitchin), we discuss the integrability conditions for four natural almost complex structures on the product bundle ${\mathcal Z}\times {\mathcal Z}\to M$, where ${\mathcal Z}$ is the twistor space…

In this paper we introduce the twistor space of a Riemannian manifold with an even Clifford structure. This notion generalizes the twistor space of quaternion-Hermitian manifolds and weak-Spin(9) structures. We also construct almost complex…