New Flavor-Kinematics Dualities and Extensions of Nonlinear Sigma Models

Abstract

Nonlinear sigma model (NLSM) based on the coset $\text{SU}(N)\times \text{SU}(N)/\text{SU}(N)$ exhibits several intriguing features at the leading $\mathcal{O}(p^2)$ in the derivative expansion, such as the flavor-kinematics duality and an extended theory controlling the single and triple soft limits. In both cases the cubic biadjoint scalar theory plays a prominent role. We extend these features in two directions. First we uncover a new extended theory for $\text{SO}(N+1)/\text{SO}(N)$ NLSM at $\mathcal{O}(p^2)$, which is a cubic bifundamental/biadjoint scalar theory. Next we provide evidence for flavor-kinematics dualities up to $\mathcal{O}(p^4)$ for both $\text{SU}(N)$ and $\text{SO}(N)$ NLSM's. In particular, we introduce a new duality building block based on the symmetric tensor ${\delta }^{ab}$ and demonstrate several flavor-kinematics dualities for 4-point amplitudes, which precisely match the soft blocks employed to soft-bootstrap the NLSM's up to $\mathcal{O}(p^4)$.

5 pages, 1 figure; matched to the published version in v2

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• New Relations for Gauge-Theory Amplitudes
• Effective Field Theories from Soft Limits
• Recursion Relations for Tree-level Amplitudes in the SU(N) Non-linear Sigma Model
• UV considerations on scattering amplitudes in a web of theories
• New Soft Theorems for Goldstone Boson Amplitudes
• A Minimally Symmetric Higgs Boson

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