Computational AdS/CFT correspondence and information loss problem
Rappel des objectifs du projet
The non-perturbative study of Yang-Mills matrix quantum mechanics and Yang-Mills matrix models. In particular, quantum black holes and cosmology can be understood in novel ways within the context of the BFSS quantum mechanics and the IKKT matrix model respectively. This study is also intimately related to the gauge/gravity duality (AdS2/CFT1 and M-(atrix) theory) and noncommutative geometry or what we call the matrix approach to quantum gravity.
Etat d’avancement des travaux
Avancement Annee 1
A systematic study of the AdS2/CFT1 correspondence in noncommutative geometry. In particular, a detailed discussion of the phase structure, emergent geometry, and emergent gravity has been put forward. Results completed and published.
More importantly, a proposed equivalence between noncommutative AdS2 from the one hand and the Yang-Mills matrix quantum models in two dimensions from the other hand is elaborated further. It is then shown that black hole evaporation presents itself as an inverse emergent gravity phase transition in a path integral formulation and thus the whole process is unitary and there is no information loss problem. This result is traced to the above stated correspondence between quantum mechanics and noncommutative geometry which is conjectured to be the correct AdS/CFT correspondence in one dimension. The geometrical/gravitational degrees of freedom in the Yang-Mills matrix phase are explicitly uncovered by going to a more fundamental description given in terms of a Yang-Mills matrix quantum mechanics. This Yang-Mills QM reduces at large number of matrices to a matrix harmonic oscillator living on the boundary. The quantized phase space of this matrix harmonic oscillator is a noncommutative pseudo-sphere whereas Euclidean AdS2 black hole configurations are given in terms of operators satisfying a non-linear sigma model constraint which establishes explicitly the absence of an information loss problem. Results presented in an international conference.
Furthermore, more work on the multitrace matrix models of noncommutative phi-four theory is done where another approach to quantum geometry is proposed. Results completed and published.
Avancement Annee 2
A systematic study of the BFSS Yang-Mills matrix quantum mechanics in various dimensions is carried out. Monte Carlo study of the lattice BFSS2 and the lattice BFSS3 is conducted. The case of lattice BFSS2 is esentially resolved while work on the case of lattice BFSS3 is still underway.
Lattice/Matrix Quantum Mechanics and Gauge/Gravity Duality: Quantum mechanics in which the degrees of freedom are matrices is known to admit, under certain conditions such as those found in the case of the celebrated BFSS/BMN models, a gravitational dual according to the general spirit of the gauge/gravity duality. This matrix quantum mechanics or mQM is characterized by gauge symmetry and supersymmetry. Lattice mQM is the study of mQM on a lattice (discretized time). This one-dimensional lattice gauge theory provides a non-perturbative definition of the dual quantum gravity. In other words, lattice mQM is the arena where the gauge/gravity duality in its simplest expression can be proved/probed non-perturbatively. Matrix quantum gravity or mQG is an approach to quantum gravity based on these matrix quantum mechanical models of string theory and on the matrix models of noncommutative geometry (NCG). Here, it is postulated that mQM and mQG are indeed dual descriptions of quantum gravity in the same sense exemplified by the AdS/CFT correspondence. It is also postulated that the mQM/mQG correspondence is a generalization of M-(atrix) theory. The mQM/mQG duality is also postulated to provide a concrete model for the AdS2/CFT1 correspondence and as a consequence it provides a complete solution of the black hole information loss problem in two dimensions. Matrix Models and Noncommutative Geometry: The high temperature limits of mQM are given by matrix models similar to the celebrated IKKT matrix model. Thus, in many cases mQG is quantized noncommutative geometry. These matrix models exhibit noncommutative emergent geometry which should be viewed as the high temperature limits of the mQM's dual gravity theory. Keywords: matrix quantum mechanics-matrix quantum mechanical models of string theory-matrix models of noncommutative geometry-gauge/gravity duality-AdS/CFT correspondence-noncommutative field theory-quantum black holes-matrix cosmology.
Résultats obtenus
A novel route to quantized geometry from multitrace matrix models.
A new proposal for the AdS2/CFT1 correspondence based on the equivalence between the noncommutative AdS2 geometry and the BFSS2 Yang-Mills matrix quantum mechanics.
The resolution of the information loss problem in quantum black holes in the context of the noncommutative AdS2/CFT1 where unitarity is firmely preserved.
The result that BFSS2 Yang-Mills matrix quantum mechanics contains no phase structure as opposed to its higher dimensional counterpart.
Publications et communications Scientifiques
Badis Ydri,
Conference: Bal-Fest Quantum Field Theory in Quantum Spacetime
DOI: 10.1142/9789811270437_0027
In book: Particles, Fields and Topology
Loubna Bouraiou, Badis Ydri
Published in: Int.J.Mod.Phys.A 37 (2022) 13, 2250079
DOI: 10.1142/S0217751X22500798
Badis Ydri
Published in: Int.J.Mod.Phys.A 37 (2022) 13, 2250078
DOI: 10.1142/S0217751X22500786
Badis Ydri
Published in: Int.J.Mod.Phys.A 37 (2022) 13, 2250077
DOI:10.1142/S0217751X22500774
Badis Ydri, Ramda Khaled, Cherine Soudani
Published in:Int.J.Mod.Phys.A 37 (2022) 10, 2250052
DOI:10.1142/S0217751X2250052X
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