Solvable Models of Domain Walls in N=1 Supergravity

A class of exactly solvable models of domain walls are worked out in D=4 ${\cal N}=1$ supergravity. We develop a method to embed globally supersymmetric theories with exact BPS domain wall solutions into supergravity, by introducing a gravitationally deformed superpotential. The gravitational deformation is natural in the spirit of maintaining the K\"ahler invariance. The solutions of the warp factor and the Killing spinor are also obtained. We find that three distinct behaviors of warp factors arise depending on the value of a constant term in the superpotential : exponentially decreasing in both sides of the wall, flat in one side and decreasing in the other, and increasing in one side and decreasing in the other. Only the first possibility gives the localized massless graviton zero mode. Models with multi-walls and models with runaway vacua are also discussed.