  We show that all tree-level amplitudes in $\varphi^p$ scalar field theory can
be represented as the $\alpha'\to0$ 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
$\varphi^p$ scalar field theory.
