Abstract
We take into account higher derivative R 4 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.
Highlights
Of the 11 dimensional supergravity [4], the dimensional black hole with SO(9) symmetry is identified with a dimensional black string which is stretching along the 11th direction
In this paper we explored the quantum nature of the black hole and black string in 11 dimensions by taking into account the higher derivative R4 corrections
We clarified the transition from the quantum black string to the quantum black hole from entropic arguments
Summary
M-theory is defined as a strong coupling limit of type IIA superstring theory, and it is well approximated by 11 dimensional supergravity in the low energy limit. We consider black hole and black string solutions in 11 dimensions. These are quite simple and it is possible to discuss leading quantum corrections to them. Where a, b, c, · · · = 0, 1, · · · , 10 are local Lorentz indices. In this action, the expansion parameter is expressed in terms of the 11 dimensional Planck length as γ. Note that the above action preserves local supersymmetry, and fermionic terms are given in refs. So if we reduce the effective action (2.1) into 10 dimensions, it corresponds to 1-loop quantum correction to the type IIA supergravity. The explicit derivation of eq (2.3) can be found in ref. [34]
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