We quantize the Hamilton equations instead of the Hamilton condition. The resulting equation has the simple form $-\D u=0$ in a fiber bundle, where the Laplacian is the Laplacian of the Wheeler-DeWitt metric provided $n\not=4$. Using then separation of variables the solutions $u$ can be expressed as products of temporal and spatial eigenfunctions, where the spatial eigenfunctions are eigenfunctions of the Laplacian in the symmetric space $SL(n,\R[])/SO(n)$. Since one can define a Schwartz space and tempered distributions in $SL(n,\R[])/SO(n)$ as well as a Fourier transform, Fourier quantization can be applied such that the spatial eigenfunctions are transformed to Dirac measures and the spatial Laplacian to a multiplication operator.

We explore an identity between two branching graphs and propose a physical meaning in the context of the gauge-gravity correspondence. From the mathematical point of view, the identity equates probabilities associated with GT, the branching graph of the unitary groups, with probabilities associated with Y, the branching graph of the symmetric groups. In order to furnish the identity with physical meaning, we exactly reproduce these probabilities as the square of three point functions involving certain hook-shaped backgrounds. We study these backgrounds in the context of LLM geometries and discover that they are domain walls interpolating two AdS spaces with different radii. We also find that, in certain cases, the probabilities match the eigenvalues of some observables, the embedding chain charges. We finally discuss a holographic interpretation of the mathematical identity through our results.

We study how conserved quantities such as angular momentum and center of mass evolve with respect to the retarded time at null infinity, which is described in terms of a Bondi-Sachs coordinate system. These evolution formulae complement the classical Bondi mass loss formula for gravitational radiation. They are further expressed in terms of the potentials of the shear and news tensors. The consequences that follow from these formulae are (1) Supertranslation invariance of the fluxes of the CWY conserved quantities. (2) A conservation law of angular momentum \`a la Christodoulou. (3) A duality paradigm for null infinity. In particular, the supertranslation invariance distinguishes the CWY angular momentum and center of mass from the classical definitions.

We show that the spinning magnetic one-brane in minimal five-dimensional supergravity admits a decoupling limit that interpolates smoothly between a self-dual null orbifold of AdS_3 \times S^2 and the near-horizon limit of the extremal Kerr black hole times a circle. We use this interpolating solution to understand the field theory dual to spinning M5 branes as a deformation of the Discrete Light Cone Quantized (DLCQ) Maldacena-Stominger-Witten (MSW) CFT. In particular, the conformal weights of the operators dual to the deformation around AdS_3 \times S^2 are calculated. We present pieces of evidence showing that a CFT dual to the four-dimensional extremal Kerr can be obtained from the deformed MSW CFT.

We exam the validity of the definition of the ADM angular momentum without the parity assumption. Explicit examples of asymptotically flat hypersurfaces in the Minkowski spacetime with zero ADM energy-momentum vector and finite non-zero angular momentum vector are presented. We also discuss the Beig-\'O Murchadha-Regge-Teitelboim center of mass and study analogous examples in the Schwarzschild spacetime