Scheme dependence of quantum gravity on de Sitter background

We extend our investigation of the IR effects on the local dynamics of matter fields in quantum gravity. Specifically we clarify how the IR effects depend on the change of the quantization scheme: different parametrization of the metric and the matter field redefinition. Conformal invariance implies effective Lorentz invariance of the matter system in de Sitter space. An arbitrary choice of the parametrization of the metric and the matter field redefinition does not preserve the effective Lorentz invariance of the local dynamics. As for the effect of different parametrization of the metric alone, the effective Lorentz symmetry breaking term can be eliminated by shifting the background metric. In contrast, we cannot compensate the matter field redefinition dependence by such a way. The effective Lorentz invariance can be retained only when we adopt the specific matter field redefinitions where all dimensionless couplings become scale invariant at the classical level. This scheme is also singled out by unitarity as the kinetic terms are canonically normalized.Comment: 20 pages, 3 figure

Green-Schwarz superstring from type IIB matrix model

We construct Green-Schwarz (GS) light-cone closed superstring theory from type IIB matrix model. A GS light-cone string action is derived from two dimensional N=8 U(n) noncommutative Yang-Mills (NCYM) by identifying noncommutative scale with string scale. Supersymmetry transformation for the light-cone gauge action is also derived from supersymmetry transformation for IIB matrix model. By identifying the physical states and interaction vertices, string theory is perturbatively reproduced.Comment: 5 pages, 3 figures, minor revision

Random Walk in the Boundary and Slow Roll in the Bulk

The slow rolling inflation is dual to the random walk of conformal zero-mode. The 2 dimensional Fokker-Planck theory predicts the slow roll parameters of 4d inflation theory. The O(N) enhancements of the two point functions, N is the e-folding number, suppress the slow roll parameters by the same magnitude. Under the gaussian approximation, FP equation boils down to a solvable first order partial differential equation. The identical equation is derived by the thermodynamic arguments . We study two types of the solutions of :(1) UV complete spacetime and (2) inflationary spacetime with power potentials. The concavity of entangled entropy dictates the potential of inflation is also concave. The maximum entropy principle favours the scenario: the universe is (a) born small and (b) grows large by inflation in the concave potentials. We predict 1-ns > 0.02(0.016) and r < 0.08(0.066) for N = 50(60)at the pivot angle 0.002(Mpc)-1. we propose a scenario to produce the curvature perturbation in the right ball park.Comment: 16 paes, 4 tables. arXiv admin note: text overlap with arXiv:2112.1356