The Infrared Structure of Nambu-Goldstone Bosons

TL;DR

This paper explores an infrared (IR) based approach to constructing effective actions for Nambu-Goldstone bosons, deriving new Ward identities, and revealing connections to extended scalar theories through soft theorems.

Contribution

It introduces a systematic IR formulation of nonlinear sigma models that derives Feynman rules and soft theorems without relying on the coset space G/H.

Findings

Derived conserved currents and Ward identities for nonlinear shift symmetry.

Established a new on-shell amplitude representation bootstrap from lower points.

Connected subleading soft limits to an extended biadjoint scalar theory.

Abstract

The construction of effective actions for Nambu-Goldstone bosons, and the nonlinear sigma model, usually requires a target coset space $G/H$. Recent progresses uncovered a new formulation using only IR data, without reference to $G/H$, by imposing the Adler's zero condition, which can be seen to originate from the superselection rule in the space of degenerate vacua. The IR construction imposes a nonlinear shift symmetry on the Lagrangian to enforce the correct single soft limit amid constraints of the unbroken group $H$. We present a systematic study on the consequence of the Adler's zero condition in correlators of nonlinear sigma model, by deriving the conserved current and the Ward identity associated with the nonlinear shift symmetry, and demonstrate how the old-fashioned current algebra emerges. The Ward identity leads to a new representation of on-shell amplitudes, which amounts to bootstrapping the higher point amplitudes from lower point amplitudes and adding new vertices to satisfy the Adler's condition. The IR perspective allows one to extract Feynman rules for the mysterious extended theory of biadjoint cubic scalars residing in the subleading single soft limit, which was first discovered using the Cachazo-He-Yuan representation of scattering amplitudes. In addition, we present the subleading triple soft theorem in the nonlinear sigma model and show that it is also controlled by on-shell amplitudes of the same extended theory as in the subleading single soft limit.