LocalizedAdS5×S5Black Holes

Abstract

We numerically construct asymptotically global AdS5 × S 5 black holes that are localised on the S 5 . These are solutions to type IIB supergravity with S 8 horizon topology that dominate the theory in the microcanonical ensemble at small energies. At higher energies, there is a first-order phase transition to AdS5-Schwarzschild×S 5 . By the AdS/CFT correspondence, this transition is dual to spontaneously breaking the SO(6) R-symmetry of N = 4 super Yang-Mills down to SO(5). We extrapolate the location of this phase transition and compute the expectation value of the resulting scalar operators in the low energy phase.

Critical behavior of the black hole/black string transition

“…Hence we expect that our results and in particular our high-precision numerical methods may be useful also for other systems such as localized black holes in Anti-deSitter spacetime [13,42]. In addition, the application of these methods to higher-dimensional versions of the system at hand should be straight-forward.…”

A proposal of the gauge theory description of the small Schwarzschild black hole in AdS5 × S5

“…According to the calculation in the gravity side [4], the transition from the large black hole to the small black hole is of first order, and the small black hole is hotter than the large black hole at the same energy. (More precisely speaking, the large BH becomes a lumpy black hole [28], and then becomes unstable.…”

“…When the Schwarzschild radius becomes of order R AdS , the BH localizes along the S 5 and can be regarded as a ten-dimensional BH. This transition is of first order [4], and the BH becomes hotter after the localization. 1 When the Schwarzschild radius becomes much smaller than R AdS , the BH should behave like the ten-dimensional Schwarzschild BH in flat spacetime, E ∼ 1 G 10,N T 7 .…”

“…A dual gravity analysis such as [4,26] may provide us with a concrete number. In the following we will not consider order one coefficients which are sensitive to this ambiguity.…”

“…The gauge field is set to zero, A t = 0, and the physical Hilbert space is obtained by acting traces of products of scalars X M (M = 1, 2, · · · , 9) on the vacuum state. 4 When we follow the usual D-brane effective theory point of view [11], the diagonal components X M,ii are regarded as the position of i-th D0-brane in R 9 , and the off-diagonal components X M,ij describe open strings connecting i-th and j-th D0-branes. Note that these strings are oriented.…”