String-like dual models for scalar theories

We show that all tree-level amplitudes in φ p scalar field theory can be represented as the α ′ → 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 φ p scalar field theory.