A finite-dimensional regularized master field that minimizes residual loop equations reproduces exact Euclidean and perturbative Minkowski results for one- and two-matrix models.
The polarised IKKT matrix model
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IKKT RG flow via Coulomb branch integration and BZJ flow reproduces the N-dependence of the axio-dilaton in IIB supergravity for D-instantons.
A regularization technique based on Berezin-Toeplitz quantization is introduced to represent curved spacetimes such as tori and the two-sphere with finite matrices in the type IIB matrix model.
Derives Minkowskian Nambu-Goto path integral for critical closed strings, proves equivalences to Polyakov and Schild forms, and obtains a causality-preserving Minkowski IKKT matrix model via regularization of the type IIB worldsheet integral.
Complex Langevin simulations of the deformed Lorentzian type IIB matrix model show emergence of smooth (3+1)-dimensional expanding spacetime with real space and time.
Derives the effective Hamiltonian in the collective field framework for three-matrix quantum mechanics models and analyzes the stability of the vacuum solution.
In the IKKT matrix model, quantum fluctuations are negligible compared to noncommutativity scales at weak coupling for Moyal-Weyl and covariant quantum spacetime backgrounds, justifying semi-classical emergent geometry.
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Regularized Master-Field Approximation for Large-$N$ Reduced Matrix Models
A finite-dimensional regularized master field that minimizes residual loop equations reproduces exact Euclidean and perturbative Minkowski results for one- and two-matrix models.