We study a c=-2 conformal field theory coupled to two-dimensional quantum gravity by means of dynamical triangulations. We define the geodesic distance r on the triangulated surface with N triangles, and show that dim[r^{d_H}]= dim[N], where the fractal dimension d_H = 3.58 +/- 0.04. This result lends support to the conjecture d_H = -2\alpha_1/\alpha_{-1}, where \alpha_{-n} is the gravitational dressing exponent of a spin-less primary field of conformal weight (n+1,n+1), and it disfavors the alternative prediction d_H = -2/\gamma_{str}. On the other hand, we find dim[l] = dim[r^2] with good accuracy, where l is the length of one of the boundaries of a circle with (geodesic) radius r, i.e. the length l has an anomalous dimension relative to the area of the surface. It is further shown that the spectral dimension d_s = 1.980 +/- 0.014 for the ensemble of (triangulated) manifolds used. The results are derived using finite size scaling and a very efficient recursive sampling technique known previously to work well for c=-2.Comment: 12 pages, LaTeX, 4 figures using psfig.sty and epsf.st

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.

We study the fractal structure of space-time of two-dimensional quantum gravity coupled to c = −2 conformal matter by means of computer simulations. We find that the intrinsic Hausdorff dimension d H = 3.58 ± 0.04. This result supports the conjecture d H = −2α 1 /α −1 , where α n is the gravitational dressing exponent of a spinless primary field of conformal weight (n + 1, n + 1), and it disfavours the alternative prediction d H = 2/|γ|. On the other hand l n ∼ r 2n for n > 1 with good accuracy, i.e. the the boundary length l has an anomalous dimension relative to the area of the surface.

We analyze the properties of mesons in (l+l)-dimensional QCD with bosonic and fermionic "quarks" in the large N, limit. We study the spectrum in detail and show that it is impossible to obtain massless mesons including boson constituents in this model. We quantitatively show how the QCD mass inequality is realized in two-dimensional QCD. We find that the mass inequality is close to being an equality even when the quarks are light. Methods for obtaining the properties of "mesons" formed from boson and/or fermion constituents are formulated in an explicit manner convenient for further study. We also analyze how the physical properties of the mesons such as confinement and asymptotic freedom are realized.PACS number(s): 12.38. Aw, ll.lO.Kk, 11.15.Pg, 12.40.Y~

Cosmological baryon asymmetry B is studied in supersymmetric standard models, assuming the electroweak reprocessing of B and L. Only when the soft supersymmetry breaking is taken into account, B is proportional to the primordial B − L in the supersymmetric standard models. The ratio B/(B − L) is found to be about one percent less than the nonsupersymmetric case. Even if the primordial B − L vanishes, scalarleptons can be more efficient than leptons to generate B provided that mixing angles θ among scalar leptons satisfy |θ| < 10 −8