Pions from higher-dimensional gluons: general realizations and stringy models

TL;DR

This paper demonstrates that scattering amplitudes of pions can be derived from higher-dimensional gluon amplitudes through a universal dimensional reduction process, connecting gauge theories, string theories, and effective field theories.

Contribution

It introduces a universal dimensional reduction method transforming gluon amplitudes into pion amplitudes, applicable across various string and field theories, revealing deep connections between them.

Findings

Dimensional reduction turns gluons into pions with Adler zero.

Stringy completions of pion amplitudes are obtained from string theory amplitudes.

Connections between gauge theories, string theories, and effective pion models are established.

Abstract

In this paper we revisit the general phenomenon that scattering amplitudes of pions can be obtained from "dimensional reduction" of gluons in higher dimensions in a more general context. We show that such "dimensional reduction" operations universally turn gluons into pions regardless of details of interactions: under such operations any amplitude that is gauge invariant and contains only local simple poles becomes one that satisfies Adler zero in the soft limit. As two such examples, we show that starting from gluon amplitudes in both superstring and bosonic string theories, the operations produce "stringy" completion of pion scattering amplitudes to all orders in $\alpha'$, with leading order given by non-linear sigma model amplitudes. Via Kawai-Lewellen-Tye relations, they give closed-stringy completion for Born-Infeld theory and the special Galileon theory, which are directly related to gravity amplitudes in closed-string theories. We also discuss how they naturally produce stringy models for mixed amplitudes of pions and colored scalars.