Axion-dilaton domain walls and fake supergravity

Dynamical systems methods are used to investigate domain-wall solutions of a two-parameter family of models in which gravity is coupled to an axion and to a dilaton with an exponential potential of either sign. A complete global analysis is presented for (i) constant axion and (ii) flat walls, including a study of bifurcations and a new exact domain-wall solution with non-constant axion. We reconsider 'fake-supergravity' issues in light of these results. We show, by example, how domain walls determine multi-valued superpotentials that branch at stationary points that are not stationary points of the potential, and we apply this result to potentials with anti-de Sitter vacua. We also show by example that 'adapted' truncation to a single- scalar model may be inconsistent, and we propose a 'generalized' fake-supergravity formalism that applies in some such cases.