Scott Collier - A matrix model for 2d de Sitter
Updated: December 25, 2024
Summary
The video delves into the development of a matrix model for 2D gravity, addressing the limitations of current string theory formulations. It explores the connections between ads2 quantum gravity, JT gravity, and low-dimensional string theories through dualities with random matrix integrals. The discussion covers key concepts such as the spectral curve, world sheet theory coupled with dilaton gravity, and the systematic computation of string amplitudes using tools like fineman diagrams and quantum volumes. Through this, the speaker aims to advance our understanding of 2D string theory and its intricate relationships with various gravitational models.
Introduction to Matrix Model for 2D Gravity
The speaker starts by thanking the organizers and introduces the work in progress on a matrix model for 2D gravity with collaborators.
Shortcomings in String Theory Formulations
Discusses the shortcomings in current formulations of string theory and highlights learnings from studying solvable models of ads quantum gravity in low dimensions.
Dualities in String Theory
Explores the duality between ads2 quantum gravity and JT gravity, as well as the dualities between low-dimensional string theories and random matrix integrals.
2D String Theory and Matrix Integrals
Describes the formulation of 2D string theory and its dualities with double-scaled matrix integrals, focusing on the spectral curve and density of eigenvalues.
World Sheet Theory and Dilaton Gravity
Discusses the world sheet theory coupled with dilaton gravity, the classical solutions, and the relationship between CFT data and local observables.
String Amplitudes and Recursion
Explores string amplitudes, recursion relations, and the systematic computation of amplitudes using fineman diagrams and quantum volumes.
Topological Recursion and Matrix Integral Loop Equations
Discusses topological recursion, loop equations of matrix integrals, and their relation to quantum volumes in JT gravity.
FAQ
Q: What are some shortcomings in current formulations of string theory discussed in the file?
A: Some shortcomings in current formulations of string theory discussed in the file include the need for a better understanding of solvable models and the exploration of dualities in low-dimensional theories.
Q: What is the duality explored between ads2 quantum gravity and JT gravity?
A: The file discusses the duality between ads2 quantum gravity and JT gravity, highlighting the connections and implications of this relationship in the context of gravitational theories.
Q: How is the formulation of 2D string theory related to double-scaled matrix integrals?
A: The file explains the formulation of 2D string theory in relation to double-scaled matrix integrals, focusing on concepts such as the spectral curve and density of eigenvalues.
Q: What is the significance of the relationship between CFT data and local observables in the context of string theory?
A: The file discusses the relationship between CFT (Conformal Field Theory) data and local observables, highlighting how this connection plays a crucial role in understanding aspects of string theory.
Q: How are string amplitudes computed systematically in the file's discussion?
A: The file discusses the systematic computation of string amplitudes using techniques like fineman diagrams and quantum volumes, providing insights into the computational methods employed in this context.
Q: What is the role of topological recursion and loop equations of matrix integrals in JT gravity?
A: The file explores the role of topological recursion and loop equations of matrix integrals in JT gravity, shedding light on the mathematical structures that underpin certain gravitational theories.
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