Quantum Near Horizon Geometry of Black 0-Brane

We investigate a bunch of D0-branes to reveal its quantum nature from the gravity side. In the classical limit, it is well described by a non-extremal black 0-brane in type IIA supergravity. The solution is uplifted to the eleven dimensions and expressed by a non-extremal M-wave solution. After reviewing the effective action for the M-theory, we explicitly solve the equations of motion for the near horizon geometry of the M-wave. As a result we derive an unique solution which includes the effect of the quantum gravity. Thermodynamic property of the quantum near horizon geometry of the black 0-brane is also studied by using Wald's formula. Combining our result with that of the Monte Carlo simulation of the dual thermal gauge theory, we find strong evidence for the gauge/gravity duality in the D0-branes system at the level of quantum gravity.Comment: 34 pages, 2 figures, section 7 is added to clarify the validity of the analyses, references added, typos corrected. Lower bound of eq. (64) and fig. 2 in section 7 are correcte

Boosted Quantum Black Hole and Black String in M-theory, and Quantum Correction to Gregory-Laflamme Instability

We take into account higher derivative R4 corrections in M-theory and construct quantum black hole and black string solutions in 11 dimensions up to the next leading order. The quantum black string is stretching along the 11th direction and the Gregory-Laflamme instability is examined at the quantum level. Thermodynamics of the boosted quantum black hole and black string are also discussed. Especially we take the near horizon limit of the quantum black string and investigate its instability quantitatively.Comment: 27 pages, 5 figures. References added and effect of the compactification for the black hole is discussed around eq. (68

Toward the Determination of R^3F^2 Terms in M-theory

Higher derivative terms in M-theory are investigated by applying the Noether method. Cancellation of variations under the local supersymmetry is examined to the order linear in F by a computer program. Structure of R^4 terms is uniquely determined and exactly matches with one-loop effective terms in type IIA superstring theory. A part of R^3F^2 terms is also determined.Comment: 13 pages, a reference adde

Quantum M-wave and Black 0-brane

The effective action of superstring theory or M-theory is approximated by supergravity in the low energy limit, and quantum corrections to the supergravity are taken into account by including higher derivative terms. In this paper, we consider equations of motion with those higher derivative terms in M-theory and solve them to derive quantum M-wave solution. A quantum black 0-brane solution is also obtained by Kaluza-Klein dimensional reduction of the M-wave solution. The quantum black 0-brane is asymptotically flat and uniquely determined by imposing appropriate conditions. The mass and the R-R charge of the quantum black 0-brane are derived by using the ADM mass and the charge formulae, and we see that only the mass is affected by the quantum correction. Various limits of the quantum black 0-brane are also considered, and especially we show that an internal energy in the near horizon limit is correctly reproduced.Comment: 26 pages. Section 6 and references adde

R^4 Corrections to Eleven Dimensional Supergravity via Supersymmetry

By applying Noether method to N=1 local supersymmetry in eleven dimensions, we obtained two candidates of R^4 corrections to the supergravity. The bosonic parts of these two completely match with the results obtained by type IIA string perturbative calculations. We also obtained 13 parameters which relate only fermionic terms.Comment: 9 pages, no figure, note adde

Gravitational Dielectric Effect and Myers Effect

In this paper we study the gravitational dielectric phenomena of a D2-brane in the background of Kaluza-Klein monopoles and D6-branes. In both cases the spherical D2-brane with nonzero radius becomes classical solution of the D2-brane action. We also investigate the gravitational Myers effect in the background of D6-branes. This phenomenon occurs since the tension of the D2-brane balances with the repulsive force between D0-branes and D6-branes.Comment: 17 pages, 4 figures, The argument on the stability of the spehrical D2-D0 bound state is modified and clarified in the appendix, The effect of background R-R field are included, reference added, version appeared in PR