The discovery of the fact that black holes radiate particles and eventually evaporate led Hawking to pose the well-known information loss paradox. This paradox caused a long and serious debate since it claims that the fundamental laws of quantum mechanics may be violated. A possible cure appeared recently from superstring theory, a consistent theory of quantum gravity: if the holographic description of a quantum black hole based on the gauge/gravity duality is correct, the information is not lost and quantum mechanics remains valid. Here we test this gauge/gravity duality on a computer at the level of quantum gravity for the first time. The black hole mass obtained by Monte Carlo simulation of the dual gauge theory reproduces precisely the quantum gravity effects in an evaporating black hole. This result opens up totally new perspectives towards quantum gravity since one can simulate quantum black holes through dual gauge theories.
We study theories with SU (2|4) symmetry, which include the plane wave matrix model, 2 + 1 SYM on R × S 2 and N = 4 SYM on R × S 3 /Z k . All these theories possess many vacua. From Lin-Maldacena's method which gives the gravity dual of each vacuum, it is predicted that the theory around each vacuum of 2 + 1 SYM on R × S 2 and N = 4 SYM on R × S 3 /Z k is embedded in the plane wave matrix model. We show this directly on the gauge theory side. We clearly reveal relationships among the spherical harmonics on S 3 , the monopole harmonics and the harmonics on fuzzy spheres. We extend the compactification (the T-duality) in matrix models a la Taylor to that on One can see from (D.8) that in the N 0 → ∞ limit, this formula reduces to N 0 tr(
We argue that the confined and deconfined phases in gauge theories are connected by a partially deconfined phase (i.e. SU(M ) in SU(N ), where M < N , is deconfined), which can be stable or unstable depending on the details of the theory. When this phase is unstable, it is the gauge theory counterpart of the small black hole phase in the dual string theory. Partial deconfinement is closely related to the Gross-Witten-Wadia transition, and is likely to be relevant to the QCD phase transition.The mechanism of partial deconfinement is related to a generic property of a class of systems. As an instructive example, we demonstrate the similarity between the Yang-Mills theory/string theory and a mathematical model of the collective behavior of ants [Beekman et al., Proceedings of the National Academy of Sciences, 2001]. By identifying the D-brane, open string and black hole with the ant, pheromone and ant trail, the dynamics of two systems closely resemble with each other, and qualitatively the same phase structures are obtained.
We perform a systematic, large-scale lattice simulation of D0-brane quantum mechanics. The large-N and continuum limits of the gauge theory are taken for the first time at various temperatures 0.4 ≤ T ≤ 1.0. As a way to test the gauge/gravity duality conjecture we compute the internal energy of the black hole as a function of the temperature directly from the gauge theory. We obtain a leading behavior that is compatible with the supergravity result E/N 2 = 7.41T 14/5 : the coefficient is estimated to be 7.4 ± 0.5 when the exponent is fixed and stringy corrections are included. This is the first confirmation of the supergravity prediction for the internal energy of a black hole at finite temperature coming directly from the dual gauge theory. We also constrain stringy corrections to the internal energy.
We investigate relationship between a gauge theory on a principal bundle and that on its base space. In the case where the principal bundle is itself a group manifold, we also study relations of those gauge theories with a matrix model obtained by dimensionally reducing them to zero dimensions. First, we develop the dimensional reduction of YangMills (YM) on the total space to YM-higgs on the base space for a general principal bundle. Second, we show a relationship that YM on an SU (2) bundle is equivalent to the theory around a certain background of YM-higgs on its base space. This is an extension of our previous work [29], in which the same relationship concerning a U (1) bundle is shown. We apply these results to the case of SU (n + 1) as the total space. By dimensionally reducing YM on SU (n + 1), we obtain YM-higgs on SU (n + 1)/SU (n) ≃ S 2n+1 and on SU (n + 1)/(SU (n) × U (1)) ≃ CP n and a matrix model. We show that the theory around each monopole vacuum of YM-higgs on CP n is equivalent to the theory around a certain vacuum of the matrix model in the commutative limit. By combining this with the relationship concerning a U (1) bundle, we realize YM-higgs on SU (n + 1)/SU (n) ≃ S 2n+1 in the matrix model. We see that the relationship concerning a U (1) bundle can be interpreted as Buscher's
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