Lagrangian constraints and renormalization of 4D gravity

It has been proposed in \cite{Park:2014tia} that 4D Einstein gravity becomes effectively reduced to 3D after solving the Lagrangian analogues of the Hamiltonian and momentum constraints of the Hamiltonian quantization. The analysis in \cite{Park:2014tia} was carried out at the classical/operator level. We review the proposal and make a transition to the path integral account. We then set the stage for explicitly carrying out the two-loop renormalization procedure of the resulting 3D action. We also address a potentially subtle issue in the gravity context concerning whether renormalizability does not depend on the background around which the original action is expanded.Comment: 40 pages, 5 figures, minor corrections, version to appear in JHE

Reduction of BTZ spacetime to hypersurfaces of foliation

We reduce the BTZ spacetime to two kinds of hypersurfaces of foliation: one having a fixed radial coordinate and the other a fixed angular coordinate. The radial reduction leads to a Liouville type theory, and confirms, from the first principle, the expectation laid out in the literature. In the other endeavor, the angular reduction of the 3D gravity is carried out in two different ways; the first again yields a Liouville type theory (different from that of the radial reduction) and the second yields a 2D interacting quantum field theory with quartic potential. Finally we discuss potential implications of our result for the Equivalence Principle and Purity of Hawking radiation.Comment: 16 pages, minor corrections, version that will appear in JHE

Absorption of a Quantum in a D1/D5 System

In {\em Nucl. Phys.} B {\bf 615}, 285 (2001) [arXiv:hep-th/0107113], the wave equation for a minimally coupled scalar was studied in the geometry of a D1-D5 system with non-zero angular momentum. The probability for a quantum to enter the throat was computed by taking small a parameter \g which is associated with the value of the angular momentum. In the leading order in \g, the result was found to agree with the dual CFT result. In this note, we report on an observation that there are corrections of higher order in \g. Our results should be useful for determining the higher order correction terms that the dual CFT needs in order to incorporate the presence of the `capped' geometry.Comment: 16 page

N2N^2 entropy of 4D N=4 SYM

We employ localization technique to derive $N^2$ entropy scaling of four dimensional N=4 SYM theory.Comment: 19 pages, latex, clarifications/explanations added, refs added, a version that will appear in NP