Computational Holographic Geometry A: Tensor Networks as Computational Bridge for Geometry-Physics Duality
zhou, changzheng, ZIQING zhou
This paper systematically discusses the core role and computational methods of tensor networks in the study of geometry-physics duality. By analyzing the unified mathematical structure of tensor networks in multi-scale entanglement renormalization, lattice field theory compression, and algebraic equation solving, we establish their position as computational bridges in AdS/CFT duality, gauge theory, and string theory compactification. We focus on exploring the intrinsic connections between matrix product states, tensor contraction algorithms, and geometric invariant computations, providing a unified theoretical framework and numerical implementation pathways for future research. This paper emphasizes tensor networks as a mathematical language that effectively connects continuous geometric structures with discrete physical models, offering a new computable perspective for understanding quantum gravity and gauge duality.
•Nov 18, 2025•0 citations