We derive the Weyl anomaly in two dimensional space-time by considering the Dirac sea regularized some negatively counted formally bosonic extra species.In fact we calculate the trace of the energy-momentum tensor of the Dirac sea in a background gra
vitational field. It has to be regularized, since otherwise the Dirac sea is bottomless and thus causes divergence. The new regularization method consists in adding various massive species some of which are to be counted negative in the Dirac sea.The mass term in the Lagrangian of the regularization fields have a dependence on the background gravitational field.
We develop the idea for a new string field theory of ours that was proposed earlier in a very rudimentary form in a talk in the Symposium of Tohwa University [1]. The main point is to describe the system of strings in the Universe by means of the ima
ges of the derivatives of the right and left mover parts of the 26-position vector on the strings w.r.t. tau. The major progress since the Tohwa-talks [1] is to imagine a discretization of the variables on which right and left movers respectively depend. We then observe that, by using only the descritized even-numbered sites, we can set the commutation rules for second quantization without any contradiction. In fact we can quantize the objects described by these even numbered images. A light-cone frame description of the string field theory in this way is presented.
In N=1 supergravity supersymmetric (SUSY) and non-supersymmetric Minkowski vacua originating in the hidden sector can be degenerate. In the supersymmetric phase in flat Minkowski space non-perturbative supersymmetry breakdown may take place in the ob
servable sector, inducing a non-zero and positive vacuum energy density. Assuming that such a supersymmetric phase and the phase in which we live are degenerate, we estimate the value of the cosmological constant. We argue that the observed value of the dark energy density can be reproduced in the Split-SUSY scenario of the supersymmetry breaking if the SUSY breaking scale is of order of 10^{10} GeV.
It is well known that global symmetries protect local supersymmetry and a zero value for the cosmological constant in no--scale supergravity. The breakdown of these symmetries, which ensure the vanishing of the vacuum energy density, results in a set
of degenerate vacua with broken and unbroken supersymmetry leading to the natural realisation of the multiple point principle (MPP). Assuming the degeneracy of vacua with broken and unbroken SUSY in the hidden sector we estimate the value of the cosmological constant. We argue that the observed value of the dark energy density can be reproduced in the split-SUSY scenario if the SUSY breaking scale is of the order of 10^{10} GeV.
