Related papers: Curvature and Gravity Actions for Matrix Models
We study the geometrical meaning of higher-order terms in matrix models of Yang-Mills type in the semi-classical limit, generalizing recent results arXiv:1003.4132 to the case of 4-dimensional space-time geometries with general Poisson…
We verify explicitly that UV/IR mixing for noncommutative gauge theory can be understood in terms of an induced gravity action, as predicted by the identification [1] of gravity within matrix models of NC gauge theory. More precisely, we…
Matrix models of Yang-Mills type induce an effective gravity theory on 4-dimensional branes, which are considered as models for dynamical space-time. We review recent progress in the understanding of this emergent gravity. The metric is not…
We derive new representations of the Einstein-Hilbert action in which graviton perturbation theory is immensely simplified. To accomplish this, we recast the Einstein-Hilbert action as a theory of purely cubic interactions among gravitons…
A introductory review to emergent noncommutative gravity within Yang-Mills Matrix models is presented. Space-time is described as a noncommutative brane solution of the matrix model, i.e. as submanifold of \R^D. Fields and matter on the…
The Einstein-Hilbert action (and thus the dynamics of gravity) can be obtained by combining the principle of equivalence, special relativity and quantum theory in the Rindler frame and postulating that the horizon area must be proportional…
A mechanism for emergent gravity on brane solutions in Yang-Mills matrix models is exhibited. Newtonian gravity and a partial relation between the Einstein tensor and the energy-momentum tensor can arise from the basic matrix model action,…
The 3+1-dimensional Einstein-Hilbert action is obtained from the 1-loop effective action on noncommutative branes in the IIB or IKKT matrix model. The presence of compact fuzzy extra dimensions ${\cal K}$ as well as maximal supersymmetry of…
The gravitational dynamics of 3+1 dimensional covariant quantum spacetime in the IKKT or IIB matrix model is studied at one loop, combining the Yang-Mills-type matrix action with the induced Einstein-Hilbert action. This combined action…
The Einstein-Hilbert action has a bulk term and a surface term (which arises from integrating a four divergence). I show that one can obtain Einstein's equations from the surface term alone. This leads to: (i) a novel, completely self…
The large-N reduced models have been proposed as the nonperturbative formulation of the superstring theory. One of the most promising candidates is the IIB matrix model. While there have been a lot of interesting discoveries of the IIB…
The starting point of this work is the original Einstein action, sometimes called the Gamma squared action. Continuing from our previous results, we study various modified theories of gravity following the Palatini approach. The metric and…
We consider general curvature-invariant modifications of the Einstein-Hilbert action that become important only in regions of extremely low space-time curvature. We investigate the far future evolution of the universe in such models,…
A matrix model on a D-dimensional Euclidean space is introduced as a generalization of random matrix models and as a non-perturbative definition of discretized closed string theory. The free energy of the matrix model is formally derived to…
The curvature of brane solutions in Yang-Mills matrix models is expressed in terms of conserved currents associated with global symmetries of the model. This implies a relation between the Ricci tensor and the energy-momentum tensor due to…
We derive the equations of motion that arise from the one-loop effective action for the geometry of 3+1 dimensional quantum branes in the IKKT matrix model. These equations are cast into the form of generalized Einstein equations, with…
The careful analysis of the duality properties of Riemann's curvature tensor points to possibility of extension of Einstein's General Relativity to the nonabelian Yang-Mills theory. The motion equations of the theory are Yang-Mills'…
A Yang-Mills type gauge theory of gravity is shown to have a structure richer than that of Einstein's General Theory of Relativity. By elevating the full connections to independent dynamical gauge fields, the theory admits non-trivial…
Recent progress in the understanding of gravity on noncommutative spaces is discussed. A gravity theory naturally emerges from matrix models of noncommutative gauge theory. The effective metric depends on the dynamical Poisson structure,…
It is well known that Einstein's equations assume a simple polynomial form in the Hamiltonian framework based on a Yang-Mills phase space. We re-examine the gravitational dynamics in this framework and show that {\em time} evolution of the…