  A world-volume model of non-critical 3-brane is quantized in a strong
coupling phase where fluctuations of the conformal mode become dominant. This
phase, called the conformal-mode dominant phase, is realized at the very high
energy far beyond the Planck mass scale. We separately treat the conformal mode
and the traceless mode and quantize the conformal mode "non-perturbatively",
while the traceless mode is treated in the perturbation which is renormalizable
and asymptotically free. In the conformal-mode dominant phase, the coupling of
the traceless mode vanishes and the world-volume dynamics is described as a
four dimensional conformal field theory (CFT_4). We canonically quantize this
model on R*S^3 where the dynamical metric fields are expanded using spherical
tensor harmonics on S^3. Conformal charges and conformal algebra are
constructed. They give strong constraints on physical states. We find that all
negative-metric modes are related to positive-metric modes through the charges
so that they are not independent physical modes themselves. An infinite number
of physical states satisfying the conformal invariance conditions are
constructed. In appendix, we construct spherical vector, tensor harmonics on
S^3 in the useable form using Wigner D-functions and Clebsch-Gordan
coefficients and calculate integrals of their products.

High Energy Physics - Theory