Soft Bootstrap and Effective Field Theories

Abstract

The soft bootstrap program aims to construct consistent effective field theories (EFT's) by recursively imposing the desired soft limit on tree-level scattering amplitudes through on-shell recursion relations. A prime example is the leading two-derivative operator in the EFT of $\text{SU}(N)\times \text{SU}(N)/\text{SU}(N)$ nonlinear sigma model (NLSM), where $\mathcal{O}(p^2)$ amplitudes with an arbitrary multiplicity of external particles can be soft-bootstrapped. We extend the program to $\mathcal{O}(p^4)$ operators and introduce the "soft blocks," which are the seeds for soft bootstrap. The number of soft blocks coincides with the number of independent operators at a given order in the derivative expansion and the incalculable Wilson coefficient emerges naturally. We also uncover a new soft-constructible EFT involving the "multi-trace" operator at the leading two-derivative order, which is matched to $\text{SO}(N+1)/\text{SO}(N)$ NLSM. In addition, we consider Wess-Zumino-Witten (WZW) terms, the existence of which, or the lack thereof, depends on the number of flavors in the EFT, after a novel application of Bose symmetry. Remarkably, we find agreements with group-theoretic considerations on the existence of WZW terms in $\text{SU}(N)$ NLSM for $N\ge 3$ and the absence of WZW terms in $\text{SO}(N)$ NLSM for $N\ne 5$.

41 pages + appendices, 13 figures; typos corrected in v3

References in corpus (10)

• Effective Field Theories from Soft Limits
• Operator bases, $S$-matrices, and their partition functions
• A Periodic Table of Effective Field Theories
• Effective Field Theory Amplitudes the On-Shell Way: Scalar and Vector Couplings to Gluons
• Perturbiner Methods for Effective Field Theories and the Double Copy
• New Formulas for Amplitudes from Higher-Dimensional Operators
• The Infrared Structure of Exceptional Scalar Theories
• Taming higher-derivative interactions and bootstrapping gravity with soft theorems
• Universal Relations in Composite Higgs Models
• New Factorization Relations for Non-Linear Sigma Model Amplitudes

Cited by in corpus (28)

• The electroweak effective field theory from on-shell amplitudes
• The SAGEX Review on Scattering Amplitudes, Chapter 11: Soft Theorems and Celestial Amplitudes
• Enumerating higher-dimensional operators with on-shell amplitudes
• Geometric Soft Theorems
• Simple encoding of higher derivative gauge and gravity counterterms
• New Soft Theorems for Goldstone Boson Amplitudes
• Complete NLO Operators in the Higgs Effective Field Theory
• Soft Matters, or the Recursions with Massive Spinors
• An EFT hunter's guide to two-to-two scattering: HEFT and SMEFT on-shell amplitudes
• Anomalous Dimensions of Effective Theories from Partial Waves
• Shift symmetries, soft limits, and the double copy beyond leading order
• Double Copy in Higher Derivative Operators of Nambu-Goldstone Bosons
• Complete NNLO Operator Bases in Higgs Effective Field Theory
• Six-pion amplitude
• Operator Counting and Soft Blocks in Chiral Perturbation Theory
• All-Multiplicity One-Loop Amplitudes in Born-Infeld Electrodynamics from Generalized Unitarity
• Amplitude/Operator Basis in Chiral Perturbation Theory
• The ChPT: top-down and bottom-up
• Nonrelativistic effective field theories with enhanced symmetries and soft behavior
• Quantum Corrections to Generic Branes: DBI, NLSM, and More
• Exploring the Landscape for Soft Theorems of Nonlinear Sigma Models
• Matter Couplings and Equivalence Principles for Soft Scalars
• Hidden Conformal Invariance of Scalar Effective Field Theories
• Soft Phonon Theorems
• Flavour-kinematics duality for Goldstone modes
• Six-meson amplitude in QCD-like theories
• ALPs, the on-shell way
• UV consistency conditions for CHY integrands