Quantum effects, brane tension, and large hierarchy in the brane world

The semiclassical Einstein equation in five dimensions with a negative cosmological constant and conformally invariant bulk matter Gelds is examined in the brane world scenario with S-1/Z(2) compactification. When numbers N-b,N-f of bosonic and fermionic fields satisfy I<<kappa>(2)l(-3)(N-b-N-f)<32I, we obtain an exact semiclassical solution which has two static branes with positive tension and for which the warp factor can be arbitrarily large. Here, <kappa>(2) is the five-dimensional gravitational constant, l is a length scale determined by the negative five-dimensional cosmological constant, and I is a dimensionless positive constant of order unity. However, in order to obtain a large warp factor, fine-tuning of brane tensions is required. Hence, in order to solve the hierarchy problem, we need to justify the fine-tuning by another new mechanism.