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

TL;DR

This paper explores semiclassical solutions in a five-dimensional brane-world model with negative cosmological constant, demonstrating how large warp factors can be achieved but require fine-tuning of brane tensions to address the hierarchy problem.

Contribution

It provides an exact semiclassical solution with two positive tension branes and large warp factors, highlighting the need for a new mechanism to justify fine tuning.

Findings

Exact semiclassical solution with large warp factor

Large warp factor requires fine tuning of brane tensions

Solution involves conformally invariant bulk matter fields

Abstract

Semiclassical Einstein's equation in five-dimension with a negative cosmological constant and conformally invariant bulk matter fields is examined in the brane world scenario with the S^1/Z_2 compactification. When numbers N_{b,f} of bosonic and fermionic fields satisfy I<\kappa^2l^{-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.