Quantum effects, brane tension, and large hierarchy in the brane world - art. no. 044008

The semiclassical Einstein equation in five dimensions with a negative cosm ological constant and conformally invariant bulk matter Gelds is examined i n 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 wit h positive tension and for which the warp factor can be arbitrarily large. Here, <kappa>(2) is the five-dimensional gravitational constant, l is a len gth scale determined by the negative five-dimensional cosmological constant , and I is a dimensionless positive constant of order unity. However, in or der to obtain a large warp factor, fine-tuning of brane tensions is require d. Hence, in order to solve the hierarchy problem, we need to justify the f ine-tuning by another new mechanism.