Proposal for the proper gravitational energy-momentum tensor

We propose a gravitational energy-momentum tensor of the general relativity obtained using Noethers theorem. It transforms as a tensor under general coordinate transformations. One of the two indices of the gravitational energy-momentum tensor labels a local Lorentz frame that satisfies the energy-momentum conservation law. The energies for a gravitational wave and a Friedmann-Lemaitre--Robertson--Walker universe are calculated as examples.Comment: A discussion on a Schwarzschild black hole is delete

Aspects of Massive Gauge Theories on Three Sphere in Infinite Mass Limit

We study the $S^3$ partition function of three-dimensional supersymmetric $\mathcal{N}=4$ U($N$) SQCD with massive matter multiplets in the infinite mass limit with the so-called Coulomb branch localization. We show that in the infinite mass limit a specific point of the Coulomb branch is selected and contributes dominantly to the partition function. Therefore, we can argue whether each multiplet included in the theory is effectively massless in this limit, even on $S^3$, and conclude that the partition function becomes that of the effective theory on the specific point of the Coulomb branch in the infinite mass limit. In order to investigate which point of the Coulomb branch is dominant, we use the saddle point approximation in the large $N$ limit because the solution of the saddle point equation can be regarded as a specific point of the Coulomb branch. Then, we calculate the partition functions for small rank $N$ and confirm that their behaviors in the infinite mass limit are consistent with the conjecture from the results in the large $N$ limit. Our result suggests that the partition function in the infinite mass limit corresponds to that of an interacting superconformal field theory.Comment: 41 pages, 5 figures; v3: published version in JHE

Landauer Conductance and Nonequilibrium Noise of One-Dimensional Interacting Electron Systems

The conductance of one-dimensional interacting electron systems is calculated in a manner similar to Landauer's argument for non-interacting systems. Unlike in previous studies in which the Kubo formula was used, the conductance is directly evaluated as the ratio of current $J$ to the chemical potential difference $\Delta \mu$ between right-going and left-going particles. It is shown that both $J$ and $\Delta \mu$ are renormalized by electron-electron (e-e) interactions, but their ratio, the conductance, is not renormalized at all if the e-e interactions are the only scattering mechanism. It is also shown that nonequilibrium current fluctuation at low frequency is absent in such a case. These conclusions are drawn for both Fermi liquids (in which quasi-particles are accompanied with the backflow) and Tomonaga-Luttinger liquids.Comment: 4 pages, No figure