New flavor-kinematics dualities and extensions of nonlinear sigma models. (English) Zbl 1473.81100
Summary: Nonlinear sigma model (nl\(\sigma\)m) based on the coset \(\mathrm{SU}(N) \times\mathrm{SU}(N)/\mathrm{SU}(N)\) 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 \(\mathrm{SO}(N+1)/\mathrm{SO}(N)\) nl\(\sigma\)m 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 \(\mathrm{SU}(N)\) and \(\mathrm{SO}(N)\) nl\(\sigma\)m’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 nl\(\sigma\)m’s up to \(\mathcal{O}(p^4)\).
MSC:
| 81T10 | Model quantum field theories |
| 35Q55 | NLS equations (nonlinear Schrödinger equations) |
| 81V05 | Strong interaction, including quantum chromodynamics |
| 81T15 | Perturbative methods of renormalization applied to problems in quantum field theory |
| 81U20 | \(S\)-matrix theory, etc. in quantum theory |
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