Ward Identity and Scattering Amplitudes for Nonlinear Sigma Models.

Area of Science:

• High Energy Physics
• Quantum Field Theory
• String Theory

Background:

• Nonlinear sigma models are fundamental in describing various physical phenomena, including particle physics and condensed matter systems.
• Understanding symmetries and their consequences, such as Ward identities, is crucial for constraining theoretical models and predicting experimental outcomes.
• Previous work often relied on current algebra or coset space constructions to derive such identities.

Purpose of the Study:

• To establish a novel Ward identity for nonlinear sigma models.
• To explore the implications of this identity for S-matrix elements and soft theorems.
• To connect generalized nonlinear shift symmetries to emergent interactions in related theories.

Main Methods:

• Development of a Ward identity utilizing generalized nonlinear shift symmetries.
• Analysis of correlation functions within the nonlinear sigma model framework.
• Application of the derived identity to tree amplitudes and soft limits.

Main Results:

• A new Ward identity for nonlinear sigma models is presented, independent of current algebra or coset space.
• The identity ensures Adler's zero for S-matrix elements and yields a quantum-level subleading single soft theorem.
• A novel Berends-Giele recursion relation and an explicit subleading single soft factor are derived for tree amplitudes.

Conclusions:

• The generalized nonlinear shift symmetry provides a powerful tool for deriving fundamental identities in nonlinear sigma models.
• The derived Ward identity offers new insights into S-matrix properties and soft theorems at all orders.
• Emergent interactions in cubic biadjoint scalar theory are shown to arise from conserved currents associated with this symmetry.