arXiv research

New natural presentation of supergravity c-map using Hodge structures.

Abstract: Generalizes supergravity c-map to quaternionic manifolds.

We consider timelike and spacelike reductions of 4D, N = 2 Minkowskian and Euclidean vector multiplets coupled to supergravity and the maps induced on the scalar geometry. In particular, we investigate (i) the (standard) spatial c-map, (ii) the temporal c-map, which corresponds to the reduction of the Minkowskian theor…

Under the action of the c-map, special Kahler manifolds are mapped into a class of quaternion-Kahler spaces. We explicitly construct the corresponding Swann bundle or hyperkahler cone, and determine the hyperkahler potential in terms of the prepotential of the special Kahler geometry.

Given a Kähler manifold $M$ endowed with a Hamiltonian Killing vector field $Z$, we construct a conical Kähler manifold $\hat{M}$ such that $M$ is recovered as a Kähler quotient of $\hat{M}$. Similarly, given a hyper-Kähler manifold $(M,g,J_1,J_2,J_3)$ endowed with a Killing vector field $Z$, Hamiltonian with respect t…

Study shows deformations of quaternionic Kähler manifolds are locally inhomogeneous.

We study the projective special Kaehler condition on groups, providing an intrinsic definition of homogeneous projective special Kaehler that includes the previously known examples. We give intrinsic defining equations that may be used without resorting to computations in the special cone, and emphasise certain associa…

We discuss the geometry of the c-map from projective special Kähler to quaternionic Kähler manifolds using the twist construction to provide a global approach to Hitchin's description. As found by Alexandrov et al. and Alekseevsky et al. this is related to the quaternionic flip of Haydys. We prove uniqueness statements…

We prove that, given a certain isometric action of a two-dimensional Abelian group A on a quaternionic Kähler manifold M which preserves a submanifold N\subset M, the quotient M'=N/A has a natural Kähler structure. We verify that the assumptions on the group action and on the submanifold N\subset M are satisfied for a …

We determine all complete projective special real surfaces. By the supergravity r-map, they give rise to complete projective special Kähler manifolds of dimension 6, which are distinguished by the image of their scalar curvature function. By the supergravity c-map, the latter manifolds define in turn complete quaternio…

We generalise the hyper-Kahler/quaternionic Kahler (HK/QK) correspondence to include para-geometries, and present a new concise proof that the target manifold of the HK/QK correspondence is quaternionic Kahler. As an application, we construct one-parameter deformations of the temporal and Euclidean supergravity c-map m…

Motivated by black hole physics in N=2, D=4 supergravity, we study the geometry of quaternionic-Kahler manifolds M obtained by the c-map construction from projective special Kahler manifolds M_s. Improving on earlier treatments, we compute the Kahler potentials on the twistor space Z and Swann space S in the complex co…

We study symmetry properties of quaternionic Kähler manifolds obtained by the HK/QK correspondence. To any Lie algebra $\mathfrak{g}$ of infinitesimal automorphisms of the initial hyper-Kähler data we associate a central extension of $\mathfrak{g}$, acting by infinitesimal automorphisms of the resulting quaternionic Kä…

The hyperKähler-quaternionic Kähler correspondence constructs quaternionic Kähler metrics from hyperKähler metrics with a rotating circle symmetry. We discuss how this may be interpreted as a combination of the twist construction with the concept of elementary deformation, surveying results of our forthcoming paper. We…

We prove that the supergravity r- and c-maps preserve completeness. As a consequence, any component H of a hypersurface {h=1} defined by a homogeneous cubic polynomial such that -d^2 h is a complete Riemannian metric on H defines a complete projective special Kahler manifold and any complete projective special Kahler m…

We show that the geometry of $4n$-dimensional quaternionic Kähler spaces with a locally free $\mathbb{R}^{n+1}$-action admits a Gibbons-Hawking-like description based on the Galicki-Lawson notion of quaternionic Kähler moment map. This generalizes to higher dimensions a four-dimensional construction, due to Calderbank …

Mathematical study of instanton corrected q-map spaces and their isometries.

We use the twistorial construction of D-instantons in Calabi-Yau compactifications of type II string theory to compute an explicit expression for the metric on the hypermultiplet moduli space affected by these non-perturbative corrections. In this way we obtain an exact quaternion-Kahler metric which is a non-trivial d…

We classify all complete projective special real manifolds with reducible cubic potential, obtaining four series. For two of the series the manifolds are homogeneous, for the two others the respective automorphism group acts with co-homogeneity one. Complete projective special real manifolds give rise to complete quate…

Construct quaternionic-Kähler metrics from special Kähler manifolds with specific BPS structure variations.

The target space geometry of abelian vector multiplets in ${\cal N}= 2$ theories in four and five space-time dimensions is called special geometry. It can be elegantly formulated in terms of Hessian geometry. In this review, we introduce Hessian geometry, focussing on aspects that are relevant for the special geometrie…

New method infers centromere locations in yeast using Hi-C data.

We study a class of supersymmetric spinning particle models derived from the radial quantization of stationary, spherically symmetric black holes of four dimensional N= 2 supergravities. By virtue of the c-map, these spinning particles move in quaternionic Kaehler manifolds. Their spinning degrees of freedom describe m…

In this paper we propose and investigate in full generality new notions of (continuous, non-isometric) symmetry on hyperkähler spaces. These can be grouped into two categories, corresponding to the two basic types of continuous hyperkähler isometries which they deform: tri-Hamiltonian isometries, on one hand, and rotat…

Defines special Joyce structures for ASK manifolds encoding real HK structures.

Defines a new modulus for Lipschitz surfaces and proves a homological duality theorem.

We consider a general 4n-dimensional quaternionic Kahler geometry with a free action of the torus T^(n+1). The toric action lifts onto the Swann bundle of the quaternionic Kahler space to a tri-holomorphic action that commutes with the standard H* action on the bundle. By matching Pedersen and Poon's generalized Gibbon…

Characterizes projective special complex manifolds using c-projective structures.

Using quaternionic Feix--Kaledin construction we provide a local classification of quaternion-Kähler metrics with a rotating $S^1$-symmetry with the fixed point set submanifold $S$ of maximal possible dimension. For any Kähler manifold $S$ equipped with a line bundle with a unitary connection of curvature proportional …

Study on quaternionic Kähler manifolds and their integrable Hermitian structures.

Unified mathematical framework for non-compact symmetric spaces with negative curvature.