A Surface Integrand for the Inverse KLT Kernel

TL;DR

This paper introduces a loop-level inverse KLT integrand that simplifies the understanding of stringy amplitudes, unifies scalar and pion scattering, and reveals structural equivalences with scalar theories.

Contribution

It constructs a novel recursive definition of the inverse KLT integrand, showing its equivalence to scalar tr$ ext{phi}^3$ theory integrands at all loop orders.

Findings

Inverse KLT integrand is a rational function of kinematic variables.

Integrand is structurally equivalent to scalar tr$ ext{phi}^3$ theory.

Unifies scalar and pion scattering via kinematic shifts.

Abstract

We propose a loop-level generalization of the inverse string theory Kawai-Lewellen-Tye (KLT) kernel: the planar inverse KLT integrand. The integrand is defined constructively via a novel Berends-Giele-like recursion that exposes the inverse KLT kernel as the simplest toy model of a ``stringy amplitude''. We show that, to all loop orders, the inverse KLT integrand is structurally equivalent to integrands in the cubic scalar tr$\phi^3$ theory. This simplicity is obscured in the conventional Feynman diagram approach, where the inverse KLT integrand receives contributions from an infinity of infinite towers of contact interactions. The inverse KLT integrand is a rational function of stringified kinematic variables and is naturally defined on the kinematic surface proposed by Arkani-Hamed et al.. It provides an elementary analogue of the surfacehedron integrand for the tr$\phi^3$ theory involving only scalar resonances and unifies the scattering of cubic scalars and pions in the non-linear sigma model (NLSM) to all loop orders via kinematic $\alpha'$-shifts.