Related papers: IIB matrix model: Emergent spacetime from the mast…
The IKKT or IIB matrix model has been proposed as a non-perturbative definition of type IIB superstring theories. It has the attractive feature that space--time appears dynamically. It is possible that lower dimensional universes dominate…
Models of Lorentz/diffeomorphism violation frequently make use of a time-dependent scalar field. We investigate space-times produced by such a field.
We propose a new method for studying the early universe in the Lorentzian version of the IIB matrix model, which is considered to be a nonperturbative formulation of superstring theory. This method is based on the idea of renormalization…
In this paper we determine the class of four-dimensional Lorentzian manifolds that can be completely characterized by the scalar polynomial curvature invariants constructed from the Riemann tensor and its covariant derivatives. We introduce…
We argue that a field theory defined on noncommutative (NC) spacetime should be regarded as a theory of gravity, which we refer to as the emergent gravity. A whole point of the emergent gravity is essentially originated from the basic…
We show that a recently proposed Yang-Mills matrix model with an auxiliary field, which is a candidate for a non-perturbative description of type IIB superstrings, captures the Euler characteristic of moduli space of Riemann surfaces. This…
We uncover a surprising correspondence between a non-perturbative formulation of three-dimensional Lorentzian quantum gravity and a hermitian two-matrix model with ABAB-interaction. The gravitational transfer matrix can be expressed as the…
The limited velocity implied by Lorentzian signature, prevents the universe to reach thermodynamic equilibrium implied by the CMB. Rapid expansion can occur by following Hawking and assuming a primordial Euclidean metric, in which case…
Here we briefly discuss lattices in Euclidean spaces and spaces of lattices, which are basic objects that can be described in terms of matrices and are important settings in classical analysis.
Large N matrices can describe covariant derivatives in curved space. Applying this interpretation to the IKKT matrix model, the field equation of gravity is derived from the matrix equation of motion. We study classical solutions of this…
We provide a short introduction to ``Lorentzian metric spaces" i.e., spacetimes defined solely in terms of the two-point Lorentzian distance. As noted in previous work, this structure is essentially unique if minimal conditions are imposed,…
We discuss how a matrix model recently shown to describe emergent gravity may contain extra degrees of freedom which reproduce some characteristics of the standard model, in particular the breaking of symmetries and the correct quantum…
The newest model for space-time is based on sub-Riemannian geometry. In this paper, we use a combination of Lorentzian and sub-Riemannian geometry, the suggest a new model which likes to its ancestors, but with the most efficient in…
Under normal circumstances most members of the general relativity community focus almost exclusively on the local properties of spacetime, such as the locally Euclidean structure of the manifold and the Lorentzian signature of the metric…
In this paper we study homogeneous backgrounds of type IIB supergravity where the underlying geometry is that of a symmetric space. We determine which ten-dimensional lorentzian symmetric spaces (up to local isometry) admit such backgrounds…
We study the spacetime structures which are described by the IIB matrix model with orientifolding. Matrix orientifolding that preserves supersymmetries yields the mirror image point with respect to a four-dimensional plane for each…
The `observer space' of a Lorentzian spacetime is the space of future-timelike unit tangent vectors. Using Cartan geometry, we first study the structure a given spacetime induces on its observer space, then use this to define abstract…
The type IIB matrix model has been proposed as a nonperturbative formulation of superstring theory. While numerical simulations of this model are essential for probing nonperturbative effects, such as the emergence of time and an expanding…
We study the classical and quantum evolution of a universe in which the matter source is a massive Dirac spinor field and the universe is described by a Bianchi type I metric. We focus attention on those classical solutions that admit a…
All Lorentzian spacetimes with vanishing invariants constructed from the Riemann tensor and its covariant derivatives are determined. A subclass of the Kundt spacetimes results and we display the corresponding metrics in local coordinates.…