Yukinori Yasui

Closed conformal Killing–Yano tensor and Kerr–NUT–de Sitter space–time uniqueness

We study spacetimes with a closed conformal Killing-Yano tensor. It is shown that the D-dimensional Kerr-NUT-de Sitter spacetime constructed by Chen-Lu- Pope is the only spacetime admitting a rank-2 closed conformal Killing-Yano tensor with a certain symmetry.

Toric Sasaki–Einstein manifolds and Heun equations

Abstract Symplectic potentials are presented for a wide class of five-dimensional toric Sasaki–Einstein manifolds, including L a , b , c which was recently constructed by Cvetic et al. The spectrum of the scalar Laplacian on L a , b , c is also studied. The eigenvalue problem leads to two Heuns differential equations and the exponents at regular singularities are directly related to the toric data. By combining knowledge of the explicit symplectic potential and the exponents, we show that the ground states, or equivalently holomorphic functions, have one-to-one correspondence with the integral lattice points in the convex polyhedral cone. The scaling dimensions of the holomorphic functions are simply given by the scalar products of the Reeb vector and the integral vectors, which are consistent with R -charges of the BPS states in the dual quiver gauge theories.

Separability of Dirac equation in higher dimensional Kerr–NUT–de Sitter spacetime

Abstract It is shown that the Dirac equations in general higher dimensional Kerr–NUT–de Sitter spacetimes are separated into ordinary differential equations.

On Spin(7) holonomy metric based on SU(3)/U(1): II

We investigate the Spin(7) holonomy metric of cohomogeneity one with the principal orbit SU(3)/U(1). A choice of U(1) in the two dimensional Cartan subalgebra is left as free and this allows manifest �3 = W(SU(3)) (= the Weyl group) symmetric formulation. We find asymptotically locally conical (ALC) metrics as octonionic gravitational instantons. These ALC metrics have orbifold singularities in general, but a particular choice of the U(1) subgroup gives a new regular metric of Spin(7) holonomy. Complex projective space CP(2) that is a supersymmetric four-cycle appears as a singular orbit. A perturbative analysis of the solution near the singular orbit shows an evidence of a more general family of ALC solutions. The global topology of the manifold depends on a choice of the U(1) subgroup. We also obtain an L 2 -normalisable harmonic 4-form in the background of the ALC metric.

Scalar Laplacian on Sasaki–Einstein manifolds Yp,q

Abstract We study the spectrum of the scalar Laplacian on the five-dimensional toric Sasaki–Einstein manifolds Y p , q . The eigenvalue equation reduces to Heuns equation, which is a Fuchsian equation with four regular singularities. We show that the ground states, which are given by constant solutions of Heuns equation, are identified with BPS states corresponding to the chiral primary operators in the dual quiver gauge theories. The excited states correspond to non-trivial solutions of Heuns equation. It is shown that these reduce to polynomial solutions in the near BPS limit.

Explicit toric metric on resolved Calabi–Yau cone

Abstract We present an explicit non-singular complete toric Calabi–Yau metric using the local solution recently found by Chen, Lu and Pope. This metric gives a new supergravity solution representing D3-branes.

Closed conformal Killing-Yano tensor and geodesic integrability

Assuming the existence of a single rank-2 closed conformal Killing–Yano tensor with a certain symmetry we show that there exists mutually commuting rank-2 Killing tensors and Killing vectors. We also discuss the condition of separation of variables for the geodesic Hamilton–Jacobi equations.

Kerr–NUT–de Sitter curvature in all dimensions

In slotting tools with exchangeable cutting inserts the insert is adapted to be clamped between two narrow jaws situated exactly above each other in the front end of a holder the lower jaw of which is formed integrally with the holder and defines the cutting seat. The upper jaw, the front portion of which reaches outside the principal part of the holder, consists of a loose member which is adapted to be inserted in a recess in the principal part of the holder, behind the cutting seat of the lower jaw, and is locked against lateral displacement. This loose member is retained in its position in the recess exclusively because of the tightening effect provided between the jaws over the clamped cutting insert.

Generalized Killing–Yano equations in D=5 gauged supergravity

Abstract We propose a generalization of the (conformal) Killing–Yano equations relevant to D = 5 minimal gauged supergravity. The generalization stems from the fact that the dual of the Maxwell flux, the 3-form ∗ F , couples naturally to particles in the background as a ‘torsion’. Killing–Yano tensors in the presence of torsion preserve most of the properties of the standard Killing–Yano tensors — exploited recently for the higher-dimensional rotating black holes of vacuum gravity with cosmological constant. In particular, the generalized closed conformal Killing–Yano 2-form gives rise to the tower of generalized closed conformal Killing–Yano tensors of increasing rank which in turn generate the tower of Killing tensors. An example of a generalized Killing–Yano tensor is found for the Chong–Cvetic–Lu–Pope black hole spacetime [Z.W. Chong, M. Cvetic, H. Lu, C.N. Pope, hep-th/0506029 ]. Such a tensor stands behind the separability of the Hamilton–Jacobi, Klein–Gordon, and Dirac equations in this background.

Sasaki-Einstein twist of Kerr-AdS black holes

Abstract We consider Kerr–AdS black holes with equal angular momenta in arbitrary odd spacetime dimensions ⩾5. Twisting the Killing vector fields of the black holes, we reproduce the compact Sasaki–Einstein manifolds constructed by Gauntlett, Martelli, Sparks and Waldram. We also discuss an implication of the twist in string theory and M-theory.