String-Like Dual Models for Scalar Theories

We show that all tree-level amplitudes in ${\phi }^p$ scalar field theory can be represented as the ${\alpha }^{\mathrm{\prime }}\to 0$ limit of an $SL(2,R)$-invariant, string-theory-like dual model integral. These dual models are constructed according to constraints that admit families of solutions. We derive these dual models, and give closed formulae for all tree-level amplitudes of any ${\phi }^p$ scalar field theory.