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NLSM $\subset$ Tr$(\phi^3)$
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abstract
Scattering amplitudes for the simplest theory of colored scalar particles - the Tr($\Phi^3$) theory - have recently been the subject of active investigations. In this letter we describe an unanticipated wider implication of this work: the Tr($\Phi^3$) theory secretly contains Non-linear Sigma Model (NLSM) amplitudes to all loop orders. The NLSM amplitudes are obtained from Tr$(\Phi^3)$ amplitudes by a unique shift of kinematic variables. We show that this shifted kinematics produces amplitudes for a cubic theory with a linear term in potential, with extrema spontaneously breaking $U(N) \to U(N-k) \times U(k)$. The Goldstone amplitudes for this theory coincide with those of pions in the $U(N) \times U(N) \to U(N)$ chiral Lagrangian to all orders in the planar limit. We also give a purely on-shell understanding of this correspondence, showing integrands defined by the kinematic shifts have the correct residues on poles and appropriately produce the Adler zero. Finally, we discuss how similar kinematic shifts produce certain infinite classes of mixed amplitudes of pions and Tr($\Phi^3$) scalars, most of which are not interpretable from the Lagrangian description.
Forward citations
Cited by 13 Pith papers
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Smooth Splitting and Zeros from On-Shell Recursion
Hidden zeros and smooth splitting in Tr phi^3, NLSM, YMS, and the special Galileon are shown to follow from on-shell recursion under improved UV falloff, yielding generalized, triple, and 4d helicity zeros.
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NLSM amplitudes from a quartic two-derivative theory
A two-field scalar theory with a single quartic two-derivative vertex reproduces all planar NLSM tree amplitudes and, up to scaleless terms, all loop integrands.
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Analytic Boundaries of Infinite-Spin-Tower Amplitudes from Hidden Zero
The exact analytic boundary of unitary infinite-spin-tower amplitudes is derived and shown to be maximal unless energy poles accumulate.
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Form factors from string amplitudes
A bosonic string disk amplitude with one closed and many open strings is proposed as a UV completion of tree-level form factors in scalar and Yang-Mills theories.
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From Cosmological Cuts to Yang--Mills Wavefunctions in de Sitter Space
Tree-level Yang-Mills de Sitter wavefunctions through six points are reconstructed from cosmological cuts into cut-detectable gluings plus a current-conservation completion, matching Feynman rules and suggesting an al...
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Curve integral formula for the M\"obius strip
A global Schwinger integral is constructed for Möbius-strip amplitudes and verified against the tropical limit of the type-I superstring Möbius amplitude.
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Correlators are simpler than wavefunctions
Equal-time correlators are simpler than wavefunctions because they come from full-spacetime integrals; this implies fewer poles, cleaner factorization, and a systematic pole expansion whose first subleading term vanishes.
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On differential operators for scalar-scaffolded gluons
Differential operators on scalar-scaffolded variables extract individual phi^3 diagrams from gluon amplitudes, and the independent mixed amplitudes are counted by Catalan numbers.
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All zeros of (super)String Theory
Scaffolding from the tachyon to higher-level string states preserves and extends the hidden zeros of string amplitudes, with extra supersymmetric zeros from the superstring.
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Universality of Colored Scalars from the Stringy KLT Kernel
Pion and colored scalar amplitudes are two readings of the same inverse KLT kernel, related by the alpha-prime shift.
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The CEGM NLSM
A systematic deformation theory for CEGM amplitudes yields generalized nonlinear sigma model amplitudes, with dimension gcd(k,n)-1 for pure deformations and an embedding of ordinary NLSM amplitudes as residues.
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On one-loop amplitudes in gauge theories
A universal expansion expresses one-loop n-gluon amplitudes in general gauge theories as scalar-loop integrands dressed by matter-dependent gauge-invariant traces.
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On the New Factorizations of Yang-Mills Amplitudes
Tree-level Yang-Mills amplitudes factorize into gluings of lower-point amplitudes when a rectangular set of Mandelstam variables vanishes, and this paper gives a rigorous CHY-based proof.
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