Emergent geometry of membranes

  title={Emergent geometry of membranes},
  author={Mathias Hudoba de Badyn and Joanna L. Karczmarek and Philippe Sabella-Garnier and Ken Huai-Che Yeh},
  journal={Journal of High Energy Physics},
A bstractIn work [1], a surface embedded in flat ℝ3 is associated to any three hermitian matrices. We study this emergent surface when the matrices are large, by constructing coherent states corresponding to points in the emergent geometry. We find the original matrices determine not only shape of the emergent surface, but also a unique Poisson structure. We prove that commutators of matrix operators correspond to Poisson brackets. Through our construction, we can realize arbitrary… 

Noncommutative spaces and matrix embeddings on flat ℝ2n + 1

A bstractWe conjecture an embedding operator which assigns, to any 2n + 1 hermitian matrices, a 2n-dimensional hypersurface in flat (2n + 1)-dimensional Euclidean space. This corresponds to precisely

Quantum (matrix) geometry and quasi-coherent states

  • H. Steinacker
  • Mathematics, Computer Science
    Journal of Physics A: Mathematical and Theoretical
  • 2021
A general framework is described which associates geometrical structures to any set of D finite-dimensional Hermitian matrices X a , a = 1, …, D, and a concept of quantum Kähler geometry arises naturally, which includes the well-known quantized coadjoint orbits such as the fuzzy sphere SN2 and fuzzy CPNn.

Kähler structure in the commutative limit of matrix geometry

We consider the commutative limit of matrix geometry described by a large-N sequence of some Hermitian matrices. Under some assumptions, we show that the commutative geometry possesses a Kähler

Commutative geometry for non-commutative D-branes by tachyon condensation

There is a difficulty in defining the positions of the D-branes when the scalar fields on them are non-abelian. We show that we can use tachyon condensation to determine the position or the shape of

Measuring finite quantum geometries via quasi-coherent states

We develop a systematic approach to determine and measure numerically the geometry of generic quantum or ‘fuzzy’ geometries realized by a set of finite-dimensional Hermitian matrices. The method is

The fuzzy space construction kit

By including branchings into the graphs, it is found that the matrix algebras of known two-dimensional fuzzy spaces are associated with unbranched graphs and represent fuzzy spaces associated with surfaces having genus 2 and higher.

Chaos, decoherence and emergent extradimensions in D-brane dynamics with fluctuations

We study, by using tools of the dynamical system theory, a fermionic string streched from a non-commutative D2-brane (stack of D0-branes in the BFSS model) to a probe D0-brane as a quantum system

Diffeomorphisms on the fuzzy sphere

Diffeomorphisms can be seen as automorphisms of the algebra of functions. In matrix regularization, functions on a smooth compact manifold are mapped to finite-size matrices. We consider how

Adiabatic transport of qubits around a black hole

We consider localized qubits evolving around a black hole following a quantum adiabatic dynamics. We develop a geometric structure (based on fibre bundles) permitting to describe the quantum states

Information metric, Berry connection, and Berezin-Toeplitz quantization for matrix geometry

The information metric and Berry connection are considered in the context of noncommutative matrix geometry and it is demonstrated that the matrix configurations of fuzzy ${S}^{n}$ ($n=2, 4) can be understood as images of the embedding functions under the Berezin-Toeplitz quantization map.



Non-commutative geometry and matrix models

These notes provide an introduction to the noncommutative matrix geometry which arises within matrix models of Yang-Mills type. Starting from basic examples of compact fuzzy spaces, a general notion

Noncommutative Riemann Surfaces

We introduce C-Algebras of compact Riemann surfaces $\Sigma$ as non-commutative analogues of the Poisson algebra of smooth functions on $\Sigma$. Representations of these algebras give rise to

Deformation Quantization of Poisson Manifolds

I prove that every finite-dimensional Poisson manifold X admits a canonical deformation quantization. Informally, it means that the set of equivalence classes of associative algebras close to the

String theory and noncommutative geometry

We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero B-field. We identify a limit in which the entire string dynamics is described by a minimally

TOPICAL REVIEW: Emergent geometry and gravity from matrix models: an introduction

An introductory review to emergent noncommutative gravity within Yang–Mills matrix models is presented. Spacetime is described as a noncommutative brane solution of the matrix model, i.e. as a

Matrix Geometry and Coherent States

We propose a novel method of finding the classical limit of the matrix geometry. We define coherent states for a general matrix geometry described by a large-$N$ sequence of $D$ Hermitian matrices

Relating branes and matrices

We construct a general map between a Dp-brane with magnetic flux and a matrix configuration of D0-branes, by showing how one can rewrite the boundary state of the Dp-brane in terms of its D0-brane

Fuzzy Riemann surfaces

We introduce C-Algebras (quantum analogues of compact Riemann surfaces), defined by polynomial relations in non-commutative variables and containing a real parameter that, when taken to zero,

Coherent states: Theory and some Applications

In this review, a general algorithm for constructing coherent states of dynamical groups for a given quantum physical system is presented. The result is that, for a given dynamical group, the