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We derive the low energy effective theory on a brane in six-dimensionalchiral supergravity. The conical 3-brane singularities are resolved byintroducing cylindrical codimension one 4-branes whose interiors are capped bya regular spacetime. The effective theory is described by the Brans-Dicke (BD)theory with the BD parameter given by $\omega_{\rm BD}=1/2$. The BD field isoriginated from a modulus which is associated with the scaling symmetry of thesystem. If the dilaton potentials on the branes preserve the scaling symmetry,the scalar field has an exponential potential in the Einstein frame. We showthat the time dependent solutions driven by the modulus in the four-dimensionaleffective theory can be lifted up to the six-dimensional exact solutions foundin the literature. Based on the effective theory, we discuss a possible way tostabilize the modulus to recover standard cosmology and also study theimplication for the cosmological constant problem.

Low energy effective theory on a regularized brane in 6D gauged chiral supergravity