2026/07/29 by Qu Cao, Zhenqi Han, Fan Zhu
Physics and Astronomy · #hep-th
12 pages, 14 figures
arxiv created 2026/07/29 · arxiv updated 2026/07/31
We revisit the well-known nonlinear sigma model (NLSM), an effective field theory describing the scattering of SU(N) Goldstone bosons and characterized by an infinite tower of two-derivative interactions. We introduce a local scalar Lagrangian involving two scalar fields ψ^± carrying opposite "polarities", whose interacting part consists of a single polynomial quartic two-derivative operator, and prove that it reproduces planar NLSM amplitudes at all loop orders. This quartic two-derivative formulation reveals a previously hidden simplicity of the NLSM: its Feynman rules involve only a single quartic interaction vertex, making the Adler zero and the leading double-soft factor manifest at all loop orders on generalized cuts and significantly improving the efficiency of high-multiplicity computations. We also suggest a possible analogous description of the NLSM + ϕ3 theory in terms of a finite tower of local interactions.