Abstract
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.
Highlights
Superstring theory is a promising candidate for the theory of quantum gravity, and it plays an important role in revealing the quantum nature of black holes
Since the M-theory is related to the type IIA superstring theory by dimensional reduction, the effective action of the M-theory should contain that of the type IIA superstring theory
In this paper we have studied the quantum nature of the bunch of D0-branes in the type IIA superstring theory
Summary
Superstring theory is a promising candidate for the theory of quantum gravity, and it plays an important role in revealing the quantum nature of black holes. In the low-energy limit, a bunch of D0-branes with additional internal energy are well described by a non-extremal black 0-brane solution in type IIA supergravity [2,3]. The purpose of this paper is to derive a quantum correction for the near-horizon geometry of the non-extremal black 0-brane directly from the gravity side. We consider the effective action for the M-theory and investigate quantum corrections to the near-horizon geometry of the non-extremal M-wave. Since we are interested in the black 0-brane that couples to the graviton gμν, the dilaton φ, and the R–R 1-form field Cμ, the relevant part of the type IIA supergravity action is given by. The near-horizon limit of the non-extremal solution of the black 0-brane (5) can be uplifted to eleven dimensions as ds121 =. This is the reason why we execute analyses of the solution in eleven dimensions
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