Multicritical Dynamical Triangulations and Topological Recursion Solve Schwinger-Dyson Equations in Two-Dimensional Models
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The behaviour of complex systems often defies simple prediction, and understanding their underlying structure remains a major challenge in theoretical physics. Hiroyuki Fuji from Kobe University, Masahide Manabe from Tottori University, and Yoshiyuki Watabiki from the Institute of Science Tokyo, investigate this problem by exploring a novel connection between two distinct approaches to quantum gravity, namely multicritical dynamical triangulations and topological recursion. Their work demonstrates that topological recursion successfully solves key equations governing both models, revealing a deep mathematical relationship and providing a powerful new tool for calculating crucial quantities that describe the geometry of spacetime. This achievement offers significant insights into the fundamental nature of gravity and potentially paves the way for a more complete understanding of quantum gravity itself. Matrix Models and Early 2D Quantum Gravity This work presents a significant advancement in understanding two-dimensional quantum gravity, matrix models, topological recursion, and related areas of theoretical physics. Researchers have compiled a comprehensive list of foundational papers and recent developments, highlighting the connections between these complex topics.,.
Topological Recursion Solves Multicritical Dynamical Triangulations This research marks a breakthrough in understanding multicritical and causal dynamical triangulations by demonstrating that topological recursion can solve the Schwinger-Dyson equations governing these models. Scientists explicitly calculated several amplitudes, revealing a deep connection between these discrete gravity models and a sophisticated analytical method. The core achievement lies in formulating a continuum theory of multicritical dynamical triangulations using mode expansions and then successfully applying topological recursion to resolve the associated equations. Researchers derived a Hamiltonian, crucial for describing the geometry of spacetime at the discrete level, and meticulously analyzed the commutation relations between the Hamiltonian and creation operators. These calculations led to a separated equation, allowing scientists to prove a proposition demonstrating that the amplitudes satisfy a recursive relation. Further analysis involved expanding the amplitudes perturbatively and examining the leading-order terms, revealing crucial information about the model’s behaviour at small values of the coupling constant.
The team demonstrated that the disk amplitude is directly related to the cosmological constants and the regular part of the one-point function, establishing a clear connection between the geometry of spacetime and the model’s parameters. This work opens new avenues for exploring the quantum nature of gravity using the powerful tools of topological recursion and discrete geometry.,.
Topological Recursion Unifies Dynamical Triangulation Models This research establishes a connection between multicritical and causal dynamical triangulations through the lens of topological recursion.
The team demonstrates that topological recursion successfully solves the Schwinger-Dyson equations governing both models, providing a powerful tool for their analysis. Specifically, the work explicitly calculates several amplitudes within these frameworks, furthering understanding of their mathematical structure and potential physical interpretations. By carefully shifting operators within the mathematical formulation, the researchers were able to unify the treatment of these models and derive consistent results. The successful application of topological recursion confirms its utility in analyzing complex systems exhibiting critical behaviour, and provides a means to compute key quantities describing the geometry of these systems. The authors acknowledge that further investigation is needed to explore the physical implications of these results and suggest that exploring the behaviour of these models in higher dimensions represents a promising avenue for continued study. 👉 More information 🗞 Multicritical Dynamical Triangulations and Topological Recursion 🧠 ArXiv: https://arxiv.org/abs/2512.10519 Tags: Rohail T. As a quantum scientist exploring the frontiers of physics and technology. My work focuses on uncovering how quantum mechanics, computing, and emerging technologies are transforming our understanding of reality. I share research-driven insights that make complex ideas in quantum science clear, engaging, and relevant to the modern world. Latest Posts by Rohail T.: Quantum Computers Measure Hall Viscosity of Fractional Quantum Hall State with Hilbert-Space Truncation December 13, 2025 Statistical Study Extends Analysis of Google 2019 Quantum Supremacy Experiment and Digital Error Model December 13, 2025 Dark Matter Mounds from Supermassive Star Collapse Are Modelled with Full General-relativistic Analysis December 13, 2025