Entanglement, Yang-Mills, and the scattering matrix as an SU(N)-equivariant kernel

A bstract We study two-body scattering as an SU(N)-equivariant map acting on tensor-product representation spaces and analyze the entanglement generated by the S -matrix. This representation-theoretic perspective separates group structure from dynamics: the decomposition of R ⊗ R ′ fixes the invariant operator algebra and therefore the qualitative entangling power of the process. For particles in the fundamental representation, End SU( N ) ( N ⊗ N ) = Span{𝕀, 𝕊}, so only the identity and swap directions preserve separability, whereas generic combinations generate entanglement. Adjoint-adjoint scattering involves a larger invariant algebra involving d -tensors and is intrinsically entangling. In Yang-Mills theory one can use color-kinematics duality to show that the color kernel lies on a fixed ray of this operator space, yielding a universal maximum of the outgoing entanglement for scattering at right angles, $$ {E}_{\star}^{(2)}=\frac{3}{4} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>E</mml:mi> <mml:mo>⋆</mml:mo> <mml:mfenced> <mml:mn>2</mml:mn> </mml:mfenced> </mml:msubsup> <mml:mo>=</mml:mo> <mml:mfrac> <mml:mn>3</mml:mn> <mml:mn>4</mml:mn> </mml:mfrac> </mml:math> for SU(2) and $$ {E}_{\star}^{(3)}\simeq 0.91 $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>E</mml:mi> <mml:mo>⋆</mml:mo> <mml:mfenced> <mml:mn>3</mml:mn> </mml:mfenced> </mml:msubsup> <mml:mo>≃</mml:mo> <mml:mn>0.91</mml:mn> </mml:math> , independent of kinematics. Dimension-six operators preserve this universality, while dimension-eight deformations populate new color sectors and shift $$ {E}_{\star}^{(N)} $$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:msubsup> <mml:mi>E</mml:mi> <mml:mo>⋆</mml:mo> <mml:mfenced> <mml:mi>N</mml:mi> </mml:mfenced> </mml:msubsup> </mml:math> , suggesting that entanglement in color space functions as a tomographic probe of effective operators. In helicity space, requiring maximally entangled inputs to scatter into maximally entangled outputs uniquely selects the Yang-Mills quartic coupling and enforces the color Jacobi identity, restating the on-shell Ward constraints as conditions on entanglement preservation. Our results suggest that the information-theoretic viewpoint unifies algebraic, geometric, and dynamical aspects of scattering.