String-Like Dual Models for Scalar Theories

Abstract

We show that all tree-level amplitudes in ${\phi }^p$ scalar field theory can be represented as the ${\alpha }^{\prime }\to 0$ 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.

15 pages, 0 figures

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Cited by in corpus (12)

• Combinatorics and Topology of Kawai-Lewellen-Tye Relations
• Stokes Polytopes : The positive geometry for ${\varphi }^4$ interactions
• String amplitudes from field-theory amplitudes and vice versa
• Labelled tree graphs, Feynman diagrams and disk integrals
• String Correlators: Recursive Expansion, Integration-by-Parts and Scattering Equations
• On Positive Geometries of Quartic Interactions II : Stokes polytopes, Lower Forms on Associahedra and Worldsheet Forms
• The positive geometry for ${\varphi }^p$ interactions
• Ambitwistor Integrands from Tensionless Chiral Superstring Integrands
• Stokes Polytopes and Intersection Theory
• Towards Positive Geometry of Multi Scalar Field Amplitudes : Accordiohedron and Effective Field Theory
• On Polytopes and Generalizations of the KLT Relations
• Geometric Recursion from Polytope Triangulations and Twisted Homology