Ward Identity and Scattering Amplitudes for Nonlinear Sigma Models

Abstract

We present a Ward identity for nonlinear sigma models using generalized nonlinear shift symmetries, without introducing current algebra or coset space. The Ward identity constrains correlation functions of the sigma model such that the Adler's zero is guaranteed for $S$-matrix elements, and gives rise to a subleading single soft theorem that is valid at the quantum level and to all orders in the Goldstone decay constant. For tree amplitudes, the Ward identity leads to a novel Berends-Giele recursion relation as well as an explicit form of the subleading single soft factor. Furthermore, interactions of the cubic biadjoint scalar theory associated with the single soft limit, which was previously discovered using the Cachazo-He-Yuan representation of tree amplitudes, can be seen to emerge from matrix elements of conserved currents corresponding to the generalized shift symmetry.

5 pages

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• UV considerations on scattering amplitudes in a web of theories
• New Soft Theorems for Goldstone Boson Amplitudes
• Soft Bootstrap and Effective Field Theories
• Lie-algebraic classification of effective theories with enhanced soft limits
• The S Matrix of 6D Super Yang-Mills and Maximal Supergravity from Rational Maps
• The Infrared Structure of Nambu-Goldstone Bosons
• New Flavor-Kinematics Dualities and Extensions of Nonlinear Sigma Models
• Double Copy in Higher Derivative Operators of Nambu-Goldstone Bosons
• Universal Imprints of a Pseudo-Nambu-Goldstone Higgs Boson
• Operator Counting and Soft Blocks in Chiral Perturbation Theory
• Universal Relations in Composite Higgs Models
• The Infrared Structure of Exceptional Scalar Theories
• Higher-order tree-level amplitudes in the nonlinear sigma model
• Nonrelativistic effective field theories with enhanced symmetries and soft behavior
• Inflationary Adler Conditions
• Exploring the Landscape for Soft Theorems of Nonlinear Sigma Models
• Soft Phonon Theorems
• Hidden Conformal Invariance of Scalar Effective Field Theories
• New Factorization Relations for Non-Linear Sigma Model Amplitudes
• Non-linearly realized discrete symmetries
• ALPs, the on-shell way
• Ward identities under the frame transformations in curved spacetime