Warped Brane Worlds in Six Dimensional Supergravity

TL;DR

The paper constructs explicit warped, supersymmetry-breaking solutions of six-dimensional Romans and Salam–Sezgin supergravity, yielding brane-world geometries with a nontrivial dilaton profile and a power-law, rather than exponential, electroweak hierarchy dependence on extra-dimensional scales. Warping modifies the KK spectrum so bulk modes can lie at TeV scales even with large internal volumes, while 3- and 4-brane boundary conditions fix most moduli under specific dilaton-flux couplings and topological constraints. A central result is that classical self-tuning of the 4D cosmological constant naturally arises from the bulk scale invariance when the brane couplings satisfy λ_3=0 and λ_4=1/2 (with the Salam–Sezgin analogue involving flux/topology), though quantum corrections and modulus stabilization remain open challenges. The work illuminates how higher-dimensional supergravity can realize brane-world scenarios with stabilized or controlled hierarchies and discusses the limitations and open issues for embedding such models in a UV-complete theory and addressing the cosmological constant problem.

Abstract

We present warped compactification solutions of six-dimensional supergravity, which are generalizations of the Randall-Sundrum warped brane world to codimension two and to a supersymmetric context. In these solutions the dilaton varies over the extra dimensions, and this makes the electroweak hierarchy only power-law sensitive to the proper radius of the extra dimensions (as opposed to being exponentially sensitive as in the RS model). Warping changes the phenomenology of these models because the Kaluza-Klein gap can be much larger than the internal space's inverse proper radius. We provide examples both for Romans' nonchiral supergravity and Salam-Sezgin chiral supergravity, and in both cases the solutions break all of the supersymmetries of the models. We interpret the solution as describing the fields sourced by a 3-brane and a boundary 4-brane (Romans' supergravity) or by one or two 3-branes (Salam-Sezgin supergravity), and we identify the topological constraints which are required by this interpretation. For both types of solutions the 3-branes are flat for all topologically-allowed values of the brane tensions. We identify the general mechanism for and limitations of the self-tuning of the effective 4D cosmological constant in higher-dimensional supergravity which these models illustrate.