Probing Scalar Effective Field Theories with the Soft Limits of Scattering Amplitudes

Abstract

We investigate the soft behaviour of scalar effective field theories (EFTs) when there is a number of distinct derivative power counting parameters, ${\rho }_1<{\rho }_2<\dots <{\rho }_Q$. We clarify the notion of an enhanced soft limit and use these to extend the scope of on-shell recursion techniques for scalar EFTs. As an example, we perform a detailed study of theories with two power counting parameters, ${\rho }_1=1$ and ${\rho }_2=2$, that include the shift symmetric generalised galileons. We demonstrate that the minimally enhanced soft limit uniquely picks out the Dirac-Born-Infeld (DBI) symmetry, including DBI galileons. For the exceptional soft limit we uniquely pick out the special galileon within the class of theories under investigation. We study the DBI galileon amplitudes more closely, verifying the validity of the recursion techniques in generating the six point amplitude, and explicitly demonstrating the invariance of all amplitudes under DBI galileon duality.

22 pages

References in corpus (10)

• Causality, Analyticity and an IR Obstruction to UV Completion
• Scattering Equations and Matrices: From Einstein To Yang-Mills, DBI and NLSM
• Effective Field Theories from Soft Limits
• On-Shell Recursion Relations for Effective Field Theories
• A Periodic Table of Effective Field Theories
• Extensions of Theories from Soft Limits
• General Embedded Brane Effective Field Theories
• Recursion relations from soft theorems
• Unification of Galileon Dualities
• A geometrical approach to degenerate scalar-tensor theories

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• An Algebraic Classification of Exceptional EFTs
• Radiation of scalar modes and the classical double copy
• Spontaneously Broken Spacetime Symmetries and the Role of Inessential Goldstones
• Scalar Fields Near Compact Objects: Resummation versus UV Completion
• Effective Field Theories and Cosmological Scattering Equations
• Symmetric Scalars
• Soft limits of the wavefunction in exceptional scalar theories
• All-Multiplicity One-Loop Amplitudes in Born-Infeld Electrodynamics from Generalized Unitarity
• Quantum Corrections to Generic Branes: DBI, NLSM, and More
• Nonrelativistic effective field theories with enhanced symmetries and soft behavior
• The analytic structure of amplitudes on backgrounds from gauge invariance and the infra-red
• A No-go Theorem for a Gauge Vector as a Space-time Goldstone
• Geometry of Multi-Flavor Galileon-Like Theories
• Inflationary Adler Conditions
• Matter Couplings and Equivalence Principles for Soft Scalars
• Hidden Conformal Invariance of Scalar Effective Field Theories
• The Boostless Bootstrap and BCFW Momentum Shifts
• Shift Symmetries for p-Forms and Mixed Symmetry Fields on (A)dS
• An Algebraic Classification of Exceptional EFTs Part II: Supersymmetry
• Internal Supersymmetry and Small-field Goldstini
• Non-perturbative aspects of galileon duality
• Symmetry Breaking Patterns for Inflation
• New Exceptional EFTs in de Sitter Space from Generalised Energy Conservation
• Extended DBI and its generalizations from graded soft theorems