Consistency Relation for multifield inflation scenario with all loop contributions

The consistency relation between non-linear parameters $f_{NL}$ and $τ_{NL}$ characterizing Non-Gaussianity generated during the inflationary period have been emerged as a useful tool which have a possibility to rule out a large class of inflationary models all at once. In our previous work, we extended the Suyama-Yamaguchi inequality up to 1-loop corrections. In this paper, we derive an inequality extended up to {\it all} loop corrections which has the same expression with the original Suyama-Yamaguchi inequality, $τ_{NL} \geq (6/5f_{NL})^2$, where the equality is not satisfied in the case of single field models any more.