The origin of spacetime as seen frm matrix model simulations时空的起源，从矩阵模型模拟.pptVIP

Extracting time evolution “critical time” SSB Consider a simpler problem : solution : representation matrices of a compact semi-simple Lie algebra with d generators Maximum is achieved for SU(2) algebra The mechanism of SSB : SO(9) - SO(3) S.-W.Kim, J.N., A.Tsuchiya, arXiv:1110.4803 Lagrange multipliers corresponding to the IR cutoffs Classical equations of motion for the Lorentzian model : We look for a Lie algebraic solution : c.f.) Euclidean model Chatzistavrakidis arXiv:1108.1107 [hep-th] Motivated by Monte Carlo results, we restrict ourselves to and look for solutions with SO(3) symmetry. From the complete list of real Lie algebras with 4 generators the one with SO(3) symmetry is UNIQUE ! Others = 0 others = 0 The unitary irreducible representations of can be classified into 2 categories 1) trivial 1d representations 2) infinite-dimensional representations the basis of the functional space Eigenfunctions of the Hamiltonian of a 1d harmonic oscillator SO(3) symmetric solutions Using a direct sum of the non-trivial representations, In what follows, Compatible with the expanding behavior ! size of the space (dimensionless) space-time noncommutativity c.f.) space-time uncertainty principle Yoneya (2000) Speculations time classical solution tcr Monte Carlo simulation SO(9) size of the space space-space noncommutativity present time accelerating expansion space-time noncommutativity Space-space NC disappears for some dynamical reason. symmetry 　of space SO(3) Black hole singularity Big bang singularity Monte Carlo simulation of supersymmetric gauge theories and matrix models Quantum effects of gravity become crucial. Two kinds of singularity predicted by Einstein’s general relativity Superstring theory Gauge-gravity correspondence “Emergent space” 1d SYM describes the space-time with black hole geometry Lorentzian matrix model Emergence of (3+1)d expanding universe Summary Future directions Extending the study of supers