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

Quantum Geometry and Diffusion

We study the diffusion equation in two-dimensional quantum gravity, and show that the spectral dimension is two despite the fact that the intrinsic Hausdorff dimension of the ensemble of two-dimensional geometries is very different from two. We determine the scaling properties of the quantum gravity averaged diffusion kernel.Comment: latex2e, 10 pages, 4 figure

Growth of uniform infinite causal triangulations

We introduce a growth process which samples sections of uniform infinite causal triangulations by elementary moves in which a single triangle is added. A relation to a random walk on the integer half line is shown. This relation is used to estimate the geodesic distance of a given triangle to the rooted boundary in terms of the time of the growth process and to determine from this the fractal dimension. Furthermore, convergence of the boundary process to a diffusion process is shown leading to an interesting duality relation between the growth process and a corresponding branching process.Comment: 27 pages, 6 figures, small changes, as publishe

Loop Equations for + and - Loops in c = 1/2 Non-Critical String Theory

New loop equations for all genera in $c = \frac{1}{2}$ non-critical string theory are constructed. Our loop equations include two types of loops, loops with all Ising spins up (+ loops) and those with all spins down ( $-$ loops). The loop equations generate an algebra which is a certain extension of $W_3$ algebra and are equivalent to the $W_3$ constraints derived before in the matrix-model formulation of 2d gravity. Application of these loop equations to construction of Hamiltonian for $c = \frac{1}{2}$ string field theory is considered.Comment: 21 pages, LaTex file, no figure

Stochastic Hamiltonian for Non-Critical String Field Theories from Double-Scaled Matrix Models

We present detailed discussions on the stochastic Hamiltonians for non-critical string field theories on the basis of matrix models. Beginning from the simplest $c=0$ case, we derive the explicit forms of the Hamiltonians for the higher critical case $k=3$ (which corresponds to $c=-22/5$) and for the case $c=1/2$, directly from the double-scaled matrix models. In particular, for the two-matrix case, we do not put any restrictions on the spin configurations of the string fields. The properties of the resulting infinite algebras of Schwinger-Dyson operators associated with the Hamiltonians and the derivation of the Virasoro and $W_3$ algebras therefrom are also investigated. Our results suggest certain universal structure of the stochastic Hamiltonians, which might be useful for an attempt towards a background independent string field theory.Comment: 70 pages, LaTeX, typographical errors are corrected, to be published in Phys. Rev.

The Harris-Luck criterion for random lattices

The Harris-Luck criterion judges the relevance of (potentially) spatially correlated, quenched disorder induced by, e.g., random bonds, randomly diluted sites or a quasi-periodicity of the lattice, for altering the critical behavior of a coupled matter system. We investigate the applicability of this type of criterion to the case of spin variables coupled to random lattices. Their aptitude to alter critical behavior depends on the degree of spatial correlations present, which is quantified by a wandering exponent. We consider the cases of Poissonian random graphs resulting from the Voronoi-Delaunay construction and of planar, ``fat'' $\phi^3$ Feynman diagrams and precisely determine their wandering exponents. The resulting predictions are compared to various exact and numerical results for the Potts model coupled to these quenched ensembles of random graphs.Comment: 13 pages, 9 figures, 2 tables, REVTeX 4. Version as published, one figure added for clarification, minor re-wordings and typo cleanu

Signature change events: A challenge for quantum gravity?

Within the framework of either Euclidian (functional-integral) quantum gravity or canonical general relativity the signature of the manifold is a priori unconstrained. Furthermore, recent developments in the emergent spacetime programme have led to a physically feasible implementation of signature change events. This suggests that it is time to revisit the sometimes controversial topic of signature change in general relativity. Specifically, we shall focus on the behaviour of a quantum field subjected to a manifold containing regions of different signature. We emphasise that, regardless of the underlying classical theory, there are severe problems associated with any quantum field theory residing on a signature-changing background. (Such as the production of what is naively an infinite number of particles, with an infinite energy density.) From the viewpoint of quantum gravity phenomenology, we discuss possible consequences of an effective Lorentz symmetry breaking scale. To more fully understand the physics of quantum fields exposed to finite regions of Euclidean-signature (Riemannian) geometry, we show its similarities with the quantum barrier penetration problem, and the super-Hubble horizon modes encountered in cosmology. Finally we raise the question as to whether signature change transitions could be fully understood and dynamically generated within (modified) classical general relativity, or whether they require the knowledge of a full theory of quantum gravity.Comment: 33 pages. 4 figures; V2: 3 references added, no physics changes; V3: now 24 pages - significantly shortened - argument simplified and more focused - no physics changes - this version accepted for publication in Classical and Quantum Gravit

Sigma model approach to string theory effective actions with tachyons

Motivated by recent discussions of actions for tachyon and vector fields related to tachyon condensation in open string theory we review and clarify some aspects of their derivation within sigma model approach. In particular, we demonstrate that the renormalized partition function $Z(T,A)$ of boundary sigma model gives the effective action for massless vectors which is consistent with string S-matrix and beta function, resolving an old problem with this suggestion in bosonic string case at the level of the leading $F^2 (dF)^2$ derivative corrections to Born-Infeld action. We give manifestly gauge invariant definition of $Z(T,A)$ in non-abelian NSR open string theory and check that its derivative reproduces the tachyon beta function in a particular scheme. We also discuss derivation of similar actions for tachyon and massless modes in closed bosonic and NSR (type 0) string theories.Comment: 26 pages, harvmac. To appear in the special issue of J. Math. Phys. on Strings, Branes and M-theory. v4: minor editorial changes, version to appear in JM

Fractal Dimensions and Scaling Laws in the Interstellar Medium and Galaxy Distributions: a new Field Theory Approach

We develop a field theoretical approach to the cold interstellar medium (ISM) and large structure of the universe. We show that a non-relativistic self- gravitating gas in thermal equilibrium with variable number of atoms or fragments is exactly equivalent to a field theory of a scalar field phi(x) with exponential self-interaction. We analyze this field theory perturbatively and non-perturbatively through the renormalization group(RG).We show scaling behaviour (critical) for a continuous range of the physical parameters as the temperature. We derive in this framework the scaling relation M(R) \sim R^{d_H} for the mass on a region of size R, and Delta v \sim R^\frac12(d_H -1) for the velocity dispersion. For the density-density correlations we find a power-law behaviour for large distances \sim |r_1 - r_2|^{2D - 6}.The fractal dimension D turns to be related with the critical exponent \nu by D = 1/ \nu. Mean field theory yields \nu = 1/2, D = 2. Both the Ising and the mean field values are compatible with the present ISM observational data:1.4\leq D \leq 2. We develop a field theoretical approach to the galaxy distribution considering a gas of self-gravitating masses on the FRW background, in quasi-thermal equi- librium. We show that it exhibits scaling behaviour by RG methods. The galaxy correlations are computed without assuming homogeneity. We find \sim r^{D-3} $. The theory allows to compute the three and higher density correlators without any assumption.We find that the connected N-points density scales as r_1^{N(D-3)}, when$ r_1 >> r_i