New Soft Theorems for Goldstone-Boson Amplitudes.

In this Letter we discuss new soft theorems for the Goldstone-boson amplitudes with nonvanishing soft limits. The standard argument is that the nonlinearly realized shift symmetry leads to the vanishing of scattering amplitudes in the soft limit, known as the Adler zero. This statement involves certain assumptions of the absence of cubic vertices and the absence of linear terms in the transformations of fields. For theories which fail to satisfy these conditions, we derive a new soft theorem which involves certain linear combinations of lower point amplitudes, generalizing the Adler zero statement. We provide an explicit example of the SU(N)/SU(N-1) sigma model which was also recently studied in the context of U(1) fibrated models. The soft theorem can be then used as an input into the modified soft recursion relations for the reconstruction of all tree-level amplitudes.

Principal Chiral Model in Correlated Electron Systems.

We discuss noncollinear magnetic phenomena whose local order parameter is characterized by more than one spin vector. By focusing on the simple cases of 2D triangular and 3D pyrochlore lattices, we demonstrate that their low-energy theories can be described by a one-parametric class of sigma models continuously interpolating between the classical Heisenberg model and the principal chiral model Tr(∂_{a}U∂_{a}U^{†}) for all U∈SU(2). The target space can be viewed as a U(1) fibration over the CP(1) space. The 3D version of our model is further generalized to break spatial and spin rotation symmetry SO(3)×SO(3)→SO(3).