Uniqueness of RS2 type thick branes supported by a scalar field

We study thick brane world models as Z_2-symmetric domain walls supported by a scalar field with an arbitrary potential V(\phi) in 5D general relativity. Under the global regularity requirement, such configurations (i) have always an AdS asymptotic far from the brane, (ii) are only possible if V(\phi) has an alternating sign and (iii) V(\phi) should satisfy a certain fine-tuning type equality. Thus a thick brane with any admissible V(\phi) is a regularized version of the RS2 brane immersed in the AdS_5 bulk. The thin brane limit is realized in a universal manner by including an arbitrary thick brane model in a one-parameter family, where the parameter "a" is associated with brane thickness; the asymptotic value of V(\phi) (related to \Lambda_5, the effective cosmological constant) remains a-independent. The problem of ordinary matter confinement on the brane is discussed for a test scalar field. Its stress-energy tensor is found to diverge at the AdS horizon for both thin and thick branes, making a serious problem for this class of brane world models.