Emergent geometry and gravity from matrix models: an introduction

  title={Emergent geometry and gravity from matrix models: an introduction},
  author={Harold C Steinacker},
  journal={Classical and Quantum Gravity},
  • H. Steinacker
  • Published 22 March 2010
  • Physics
  • Classical and Quantum Gravity
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 submanifold of . Fields and matter on the brane arise as fluctuations of the bosonic resp. fermionic matrices around such a background, and couple to an effective metric interpreted in terms of gravity. Suitable tools are provided for the description of the effective geometry in the semi-classical limit… 

Figures from this paper

Curvature and gravity actions for matrix models: II. The case of general Poisson structures

We study the geometrical meaning of higher order terms in matrix models of Yang–Mills type in the semi-classical limit, generalizing recent results (Blaschke and Steinacker 2010 Class. Quantum Grav.

Gravity and compactified branes in matrix models

A bstractA mechanism for emergent gravity on brane solutions in Yang-Mills matrix models is exhibited. Gravity and a partial relation between the Einstein tensor and the energy-momentum tensor can

Emergent gravity from hidden sectors and TT deformations

We investigate emergent gravity extending the paradigm of the AdS/CFT correspondence. The emergent graviton is associated to the (dynamical) expectation value of the energy-momentum tensor. We derive

The origin of space-time as seen from matrix model simulations

The AdS/CFT correspondence, or more generally the gauge/gravity duality, is a remarkable conjecture obtained from superstring theory with various D-brane backgrounds. According to this conjecture, a

Aspects of emergent geometry, strings, and branes in gauge / gravity duality

Author(s): Dzienkowski, Eric Michael | Advisor(s): Berenstein, David | Abstract: We explore the emergence of locality and geometry in string theories from the perspective of gauge theories using

Instantons, Twistors, and Emergent Gravity

Motivated by potential applications to holography on space-times of positive curvature, and by the successful twistor description of scattering amplitudes, we propose a new dual matrix formulation of

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

Gravity as a quantum effect on quantum space-time

Noncommutative Gravity and Quantum Field Theory on Noncommutative Curved Spacetimes

The focus of this PhD thesis is on applications, new developments and extensions of the noncommutative gravity theory proposed by Julius Wess and his group. In part one we propose an extension of

Schwarzschild geometry emerging from matrix models

We demonstrate how various geometries can emerge from Yang–Mills-type matrix models with branes, and consider the examples of Schwarzschild and Reissner–Nordström geometries. We provide an explicit



Emergent gravity from noncommutative gauge theory

We show that the matrix-model action for noncommutative U(n) gauge theory actually describes SU(n) gauge theory coupled to gravity. This is elaborated in the 4-dimensional case. The SU(n) gauge

M theory as a matrix model: A Conjecture

We suggest and motivate a precise equivalence between uncompactified 11-dimensional M theory and the N={infinity} limit of the supersymmetric matrix quantum mechanics describing D0 branes. The

Fermions and emergent noncommutative gravity

Fermions coupled to Yang-Mills matrix models are studied from the point of view of emergent gravity. We show that the simple matrix model action provides an appropriate coupling for fermions to

Emergent Gravity from Quantized Spacetime

We examine the picture of emergent gravity arising from a mas s deformed matrix model. Due to the mass deformation, a vacuum geometry turns out to be a co nstant curvature spacetime such as

Magnetic fields, branes, and noncommutative geometry

We construct a simple physical model of a particle moving on the infinite noncommutative 2-plane. The model consists of a pair of opposite charges moving in a strong magnetic field. In addition, the

On the Newtonian limit of emergent NC gravity and long-distance corrections

We show how Newtonian gravity emerges on 4-dimensional non-commutative spacetime branes in Yang-Mills matrix models. Large matter clusters such as galaxies are embedded in large-scale harmonic

Fermions and noncommutative emergent gravity II: curved branes in extra dimensions

We study fermions coupled to Yang-Mills matrix models from the point of view of emergent gravity. The matrix model Dirac operator provides an appropriate coupling for fermions to the effective

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

Cosmological solutions of emergent noncommutative gravity.

This work finds cosmological solutions of the Friedmann-Robertson-Walker type, which generically have a big bounce, and an early inflationlike phase with graceful exit, and may provide an alternative to standard cosmology.