Monte Carlo Studies of the Emergent Spacetime in the Polarized Type IIB Matrix Model

Area of Science:

• High Energy Physics
• String Theory
• Quantum Gravity

Background:

• The IKKT (or type IIB matrix) model offers a nonperturbative approach to superstring theory.
• A dual supergravity solution, the polarized IKKT model, emerged after supersymmetry-preserving mass deformation.

Purpose of the Study:

• To perform Monte Carlo simulations of the polarized IKKT model for matrix size N=2.
• To explore emergent spacetime structure by calculating observables not previously accessible.
• To investigate the model's behavior across a wide range of the deformation parameter Ω.

Main Methods:

• Monte Carlo simulations were employed for the polarized IKKT model with N=2.
• The partition function was reproduced using known results from localization methods.
• Observables were calculated to probe emergent spacetime configurations.

Main Results:

• The study reproduced the partition function using localization methods.
• A smooth connection was found between the original IKKT model's saddle point and the fuzzy sphere saddle at large Ω.
• Dominant configurations shifted to diverging commuting matrices at small Ω.

Conclusions:

• The simulations provide insights into the emergent spacetime structure of the polarized IKKT model.
• The findings bridge different regimes of the deformation parameter, linking fuzzy spheres to diverging matrices.
• This work extends previous analyses by calculating previously inaccessible observables.