Complex Langevin Simulations of the Matrix Model for Superstrings by Jun Nishimura

Explore complex Langevin simulations of the matrix model for superstrings in this comprehensive lecture by Jun Nishimura from the International Centre for Theoretical Sciences. Delve into the IKKT matrix model, its crucial properties, and the emergence of (3+1)-dimensional expanding behavior. Learn about the definition of the Lorentzian IKKT matrix model, regularization techniques, and the complex Langevin method. Discover the emergence of a smooth space-time in a new phase and its relationship to the Euclidean model. Gain insights into the phase diagram, time evolution extraction, and the spontaneous symmetry breaking of SO(10). This 89-minute talk covers advanced topics in nonperturbative approaches to quantum gravity, string theory, and holography, providing a deep dive into cutting-edge research in theoretical physics.

04:30 pm, 19 JANUARY 2021
Complex Langevin simulations of the matrix model for superstrings
IKKT matrix model
Crucial properties of the IKKT matrix model
3. Emergence of 3+1-dim. expanding behavior 4.
1. Definition of the Lorentzian IKKT matrix model
Lorentzian Euclidean
Regularizing the Lorentzian model
IR cutoffs as a regularization
The phase diagram we consider in this talk
2. Complex Langevin method
The complex Langevin method
Complex Langevin equation
3. Emergence of 3+1-dimensional expanding behavior
Results at s,k=-1,0
Extracting time-evolution from the Lorentzian model
Emergence of 3+1-dim. expanding behavior
Confirmation of the mechanism
4. Emergence of a smooth space-time in a new phase
Exploring the phase diagram towards s, k = 0, 0
Extracting time-evolution from the Lorentzian model
A new phase appears at -1 0
Results at larger N
Expanding behavior at s,k=0,0 resembles that of typical classical solutions
5. Relationship of the new phase to the Euclidean model
The new phase is smoothly connected to the Euclidean model
Confirmation of continuity by CL simulation without IR constraints
6. Summary and Discussions
Summary
Discussions
SSB of SO10 observed by decreasing the deformation parameter mf.
In the Lorentzian case,
Summary
Expanding behavior at s,k=0,0 resembles that of typical classical solutions
Confirmation of continuity by CL simulation without IR constraints
SSB of SO10 observed by decreasing the deformation parameter mf.