Geometry in transition: a model of emergent geometry

Area of Science:

• Theoretical physics
• Quantum field theory
• Cosmology

Background:

• Matrix models are fundamental in theoretical physics, often used to explore quantum gravity and string theory.
• Understanding phase transitions is crucial for comprehending the behavior of physical systems under varying conditions, including the early Universe.

Purpose of the Study:

• To investigate the phase transitions and emergent geometrical properties of a three-matrix model with SO(3) symmetry.
• To characterize the nature of these transitions, particularly focusing on thermodynamic and fluctuation behaviors.

Main Methods:

• Analysis of a three-matrix model with quartic matrix powers and global SO(3) symmetry.
• Examination of thermodynamic quantities such as entropy and specific heat.
• Investigation of critical fluctuations and their exponents.

Main Results:

• Discovery of an exotic line of first-order-like transitions characterized by a jump in entropy.
• Observation of divergent critical fluctuations and specific heat with a critical exponent alpha=1/2.
• Identification of a low-temperature geometrical phase with fluctuating gauge fields on a sphere, transitioning to a pure matrix phase at higher temperatures.

Conclusions:

• The model exhibits a unique phase transition where geometry dynamically emerges and evaporates.
• This phenomenology provides a potential scenario for the emergence of geometry in the early Universe.
• The findings suggest that similar transitions may occur in higher-dimensional matrix models.