The Infrared Structure of Exceptional Scalar Theories

Abstract

Exceptional theories are a group of one-parameter scalar field theories with (enhanced) vanishing soft limits in the S-matrix elements. They include the nonlinear sigma model (NLSM), Dirac-Born-Infeld scalars and the special Galileon theory. The soft behavior results from the shift symmetry underlying these theories, which leads to Ward identities generating subleading single soft theorems as well as novel Berends-Giele recursion relations. Such an approach was first applied to NLSM in 1709.08639 and 1804.08629, and here we use it to systematically study other exceptional scalar field theories. In particular, using the subleading single soft theorem for the special Galileon we identify the Feynman vertices of the corresponding extended theory, which was first discovered using the Cachazo-He-Yuan representation of scattering amplitudes. Furthermore, we present a Lagrangian for the extended theory of the special Galileon, which has a rich particle content involving biadjoint scalars, Nambu-Goldstone bosons and Galileons, as well as additional flavor structure.

30 pages + appendices, 7 figures; matched to the JHEP version in v2

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• Exploring the Landscape for Soft Theorems of Nonlinear Sigma Models
• Scattering Equations and Factorization of Amplitudes II: Effective Field Theories
• New general DBI action, its solution to the paradox of the conversion of kinetic and potential energy in equal rights and their true applications to inflationary cosmology