Negative Junction Logarithms in Scalar Multipartite Entanglement

Abstract

A three-region junction in a free real relativistic scalar vacuum in $2+1$ dimensions yields a strictly negative logarithmic contribution to genuine tripartite Rényi multi-entropy for every integer $n\geq3$ and all nondegenerate sector angles. The replica subtraction exactly removes loop classes associated with a single interface. Surviving loops have positive, scale-independent weight, yielding a logarithm whose sign is fixed by the negative Rényi prefactor. The selector is empty at $n=2$. The flat-sheet Friedrichs prescription fixes the scalar operator at the nonmanifold replica apex. It yields a convergent angular spectral formula for the coefficient.