Constructing A String Theory Background Using Brane-Simplex Duality

Abstract

String theory is a candidate theory for a unified description of physics. Unification of the micro and macrocosm and also of the four fundamental forces. String theory is however plagued by conceptual potholes, chief of which is the presence of extra dimensions, large or compactified. It also lacks a consistent description of spacetime. This is the problem of quantum gravity. Causal dynamical triangulation is a framework which seeks to quantise gravity by quantising spacetime. This can be done because it accepts the geometrodynamic definition of gravitation from general relativity. The quantum of spacetime is called a simplex. Spacetime is then constructed by “gluing” these simplices together. Causal dynamical triangulation is background independent. We investigate the possibility of generating spacetime using the modes of vibrations of strings in string theory. This is done by adding a version of the Regge action, generated in causal dynamical triangulation, to the Polyakov action of bosonic string theory. After this, the equations of motion are derived from application of the Euler-Lagrange equations on the Polyakov action. The resulting differential equations are solved to generate mode expansions. From these mode expansions, we get the Virasoro operators which can be used to generate the generators of the Lorentz algebra of the theory. The Lorentz algebra of the theory then defines the dimensionality of the model. A similar process is performed for superstring theory. We thust formulate a “chimeric” string model using the Ramond-Neveu-Schwarz formalism in superstring theory. The model exhibits spacetime simplices as a type of mode expansion of the string. It is thus be background independent. There is no effect on the dimensionality on string theory by the new model.