Laplacians on Fuzzy Riemann Surfaces

Abstract

We consider the matrix regularization of scalar fields on a Riemann surface with a general gauge-field background. We propose a construction of the fuzzy version of the Laplacian.

arXiv comment23 pages

References in corpus (35)

• String Theory and Noncommutative Geometry
• M Theory As A Matrix Model: A Conjecture
• Noncommutative Geometry and Matrix Theory: Compactification on Tori
• Noncommutative Perturbative Dynamics
• A Large-N Reduced Model as Superstring
• The Spectral Action Principle
• Renormalisation of ϕ^4-theory on noncommutative R^4 in the matrix base
• Toeplitz Quantization of Kähler Manifolds and $gl(N)$ $N\to \infty$
• Noncommutative Geometry and Gravity
• Noncommutative Yang-Mills in IIB Matrix Model
• Matrix Perturbation Theory For M-theory On a PP-Wave
• Emergent Geometry and Gravity from Matrix Models: an Introduction
• Noncommutative Gauge Theory on Fuzzy Sphere from Matrix Model
• Monopoles and Solitons in Fuzzy Physics
• Topologically nontrivial field configurations in noncommutative geometry
• On the asymptotic expansion of Bergman kernel
• Scaling Limits of the Fuzzy Sphere at one Loop
• Noncommutative Gauge Theory on Fuzzy Four-Sphere and Matrix Model
• D-branes, Matrix Theory and K-homology
• Embedding of theories with SU(2|4) symmetry into the plane wave matrix model
• Noncommutative Gauge Theories on Fuzzy Sphere and Fuzzy Torus from Matrix Model
• The SPIN${}^c$ Dirac operator on high tensor powers of a line bundle
• Geometric Quantization of Vector Bundles
• Gauge Theory on Fuzzy S^2 x S^2 and Regularization on Noncommutative R^4
• Quantization of Equivariant Vector Bundles
• Noncommutative vector bundles over fuzzy CP^N and their covariant derivatives
• Information metric, Berry connection and Berezin-Toeplitz quantization for matrix geometry
• Landau-Hall States and Berezin-Toeplitz Quantization of Matrix Algebras
• $SO(4)$ Landau Models and Matrix Geometry
• Noncommutativity and Tachyon Condensation
• Existence of new nonlocal field theory on noncommutative space and spiral flow in renormalization group analysis of matrix models
• Geometry from Matrices via D-branes
• The matrix regularization for Riemann surfaces with magnetic fluxes
• Renormalization on the fuzzy sphere
• Diffeomorphisms on Fuzzy Sphere

Cited by in corpus (1)

• Regularization of matrices in the covariant derivative interpretation of matrix models