124,695 research outputs found
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
entropy of 4D N=4 SYM
We employ localization technique to derive 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
Hypersurface foliation approach to renormalization of ADM formulation of gravity
We carry out ADM splitting in the Lagrangian formulation and establish a
procedure in which (almost) all of the unphysical components of the metric are
removed by using the 4D diffeomorphism and the measure-zero 3D symmetry. The
procedure introduces a constraint that corresponds to the Hamiltonian
constraint of the Hamiltonian formulation, and its solution implies that the 4D
dynamics admits an effective description through 3D hypersurface physics. As
far as we can see, our procedure implies potential renormalizability of {the
ADM formulation of} 4D Einstein gravity for which a complete gauge-fixing in
the ADM formulation and hypersurface foliation of geometry are the key
elements. If true, this implies that the alleged unrenormalizability of 4D
Einstein gravity may be due to the presence of the unphysical fields. The
procedure can straightforwardly be applied to quantization around a flat
background; the Schwarzschild case seems more subtle. We discuss a potential
limitation of the procedure when applying it to explicit time-dependent
backgrounds.Comment: 29 pages, 3 figures, expanded for clarity, refs added, the version to
appear in EPJ
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