Cosmic time evolution and propagator from a Yang-Mills matrix model

Abstract

We consider a solution of a IKKT-type matrix model which can be considered as a 1+1-dimensional space-time with Minkowski signature and a Big Bounce-like singularity. A suitable $i\epsilon$ regularization of the Lorentzian matrix integral is proposed, which leads to the standard $i\epsilon$-prescription for the effective field theory. In particular, the Feynman propagator is recovered locally for late times. This demonstrates that a causal structure and time evolution can emerge in the matrix model, even on non-trivial geometries. We also consider the propagation of modes through the Big Bounce, and observe an interesting correlation between the post-BB and pre-BB sheets, which reflects the structure of the brane in target space.

26 apages, 1 figure. V2: pre-and post-BB correlation fixed, references added. V3: improved presentation, published version

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• Complex Langevin analysis of the space-time structure in the Lorentzian type IIB matrix model
• On the propagation across the big bounce in an open quantum FLRW cosmology
• Non-commutative $Ad{S}_2/CF{T}_1$ duality: the case of massless scalar fields
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Cited by in corpus (5)

• Progress in the numerical studies of the type IIB matrix model
• One-loop effective action and emergent gravity on quantum spaces in the IKKT matrix model
• One-loop effective action of the IKKT model for cosmological backgrounds
• Fuzzy Black Holes from Mass Generation in Matrix Compactification
• QFT on Fuzzy AdS Spaces: Classical Limit and Boundary Correlation Functions