Non-critical string field theory for 2d quantum gravity coupled to (p,q)--conformal fields

We propose a non-critical string field theory for $2d$ quantum gravity coupled to ($p$,$q$) conformal fields. The Hamiltonian is described by the generators of the $W_p$ algebra, and the Schwinger-Dyson equation is equivalent to a vacuum condition imposed on the generators of $W_p$ algebra.Comment: LaTeX, 30 pages, 6 figure

Quantization of Neveu-Schwarz-Ramond Superstring Model in 10+2-dimensional Spacetime

We construct a Neveu-Schwarz-Ramond superstring model which is invariant under supersymmetric U(1)_V * U(1)_A gauge transformations as well as the super-general coordinate, the super local Lorentz and the super-Weyl transformations on the string world-sheet. We quantize the superstring model by covariant BRST formulation a la Batalin and Vilkovisky and noncovariant light-cone gauge formulation. Upon the quantizations the model turns out to be formulated consistently in 10+2-dimensional background spacetime involving two time dimensions.Comment: 1+61 pages, no figures, LaTe

The bosonic string and superstring models in 26+2 and 10+2 dimensional space--time, and the generalized Chern-Simons action

We have covariantized the Lagrangians of the U(1)_V * U(1)_A models, which have U(1)_V * U(1)_A gauge symmetry in two dimensions, and studied their symmetric structures. The special property of the U(1)_V * U(1)_A models is the fact that all these models have an extra time coordinate in the target space-time. The U(1)_V * U(1)_A models coupled to two-dimensional gravity are string models in 26+2 dimensional target space-time for bosonic string and in 10+2 dimensional target space-time for superstring. Both string models have two time coordinates. In order to construct the covariant Lagrangians of the U(1)_V * U(1)_A models the generalized Chern-Simons term plays an important role. The supersymmetric generalized Chern-Simons action is also proposed. The Green-Schwarz type of U(1)_V * U(1)_A superstring model has another fermionic local symmetry as well as \kappa-symmetry. The supersymmetry of target space-time is different from the standard one.Comment: 27 pages, no figure

A modified Friedmann equation

We recently formulated a model of the universe based on an underlying W3-symmetry. It allows the creation of the universe from nothing and the creation of baby universes and wormholes for spacetimes of dimension 2, 3, 4, 6 and 10. Here we show that the classical large time and large space limit of these universes is one of exponential fast expansion without the need of a cosmological constant. Under a number of simplifying assumptions our model predicts that w=-1.2 in the case of four-dimensional spacetime. The possibility of obtaining a w-value less than -1 is linked to the ability of our model to create baby universes and wormholes.Comment: Clarifying comment on page

Creating 3, 4, 6 and 10-dimensional spacetime from W3 symmetry

We describe a model where breaking of W3 symmetry will lead to the emergence of time and subsequently of space. Surprisingly the simplest such models which lead to higher dimensional spacetimes are based on the four "magical" Jordan algebras of 3x3 Hermitian matrices with real, complex, quaternion and octonion entries, respectively. The simplest symmetry breaking leads to universes with spacetime dimensions 3, 4, 6, and 10

CDT and the Big Bang

We describe a CDT-like model where breaking of W3 symmetry will lead to the emergence of time and subsequently of space. Surprisingly the simplest such models which lead to higher dimensional spacetimes are based on the four "magical" Jordan algebras of 3x3 Hermitian matrices with real, complex, quaternion and octonion entries, respectively. The simplest symmetry breaking leads to universes with spacetime dimensions 3, 4, 6, and 10

A model for emergence of space and time

We study string field theory (third quantization) of the two-dimensional model of quantum geometry called generalized CDT ("causal dynamical triangulations"). Like in standard non-critical string theory the so-called string field Hamiltonian of generalized CDT can be associated with W-algebra generators through the string mode expansion. This allows us to define an "absolute" vacuum. "Physical" vacua appear as coherent states created by vertex operators acting on the absolute vacuum. Each coherent state corresponds to specific values of the coupling constants of generalized CDT. The cosmological "time" only exists relatively to a given "physical" vacuum and comes into existence before space, which is created because the "physical" vacuum is unstable. Thus each CDT "universe" is created as a "Big Bang" from the absolute vacuum, its time evolution is governed by the CDT string field Hamiltonian with given coupling constants, and one can imagine interactions between CDT universes with different coupling constants ("fourth quantization"

Scale-dependent Hausdorff dimensions in 2d gravity

By appropriate scaling of coupling constants a one-parameter family of ensembles of two-dimensional geometries is obtained, which interpolates between the ensembles of (generalized) causal dynamical triangulations and ordinary dynamical triangulations. We study the fractal properties of the associated continuum geometries and identify both global and local Hausdorff dimensions.Comment: 12 pages, 3 figure

Quantization of Bosonic String Model in 26+2-dimensional Spacetime

We investigate the quantization of the bosonic string model which has a local U(1)_V * U(1)_A gauge invariance as well as the general coordinate and Weyl invariance on the world-sheet. The model is quantized by Lagrangian and Hamiltonian BRST formulations {\'a} la Batalin, Fradkin and Vilkovisky and noncovariant light-cone gauge formulation. Upon the quantization the model turns out to be formulated consistently in 26+2-dimensional background spacetime involving two time-like coordinates.Comment: 1+39 pages, no figures, LaTe