(Phenomenology/Lattice-Compatible) SU(3) MχPT HD up to O $$ \mathcal{O} $$ (p4) and the O $$ \mathcal{O} $$ (R4)-Large-N Connection

Obtaining the values of the coupling constants of the low energy effective theory corresponding to QCD, compatible with experimental data, even in the (vector) mesonic sector from (the $$ \mathcal{M} $$ -theory uplift of) a UV-complete string theory dual, has thus far been missing in the literature. We take the first step in this direction by obtaining the values of the coupling constants of the $$ \mathcal{O} $$ (p4) χPT Lagrangian in the chiral limit involving the NGBs and ρ meson (and its flavor partners) from the $$ \mathcal{M} $$ -theory/type IIA dual of large-N thermal QCD, inclusive of the $$ \mathcal{O} $$ (R4) corrections. We observe that ensuring compatibility with phenomenological/lattice results (the values) as given in [1], requires a relationship relating the $$ \mathcal{O} $$ (R4) corrections and large-N suppression. In other words, QCD demands that the higher derivative corrections and the large-N suppressed corrections in its M/string theory dual, are related. As a bonus, we explicitly show that the $$ \mathcal{O} $$ (R4) corrections in the UV to the $$ \mathcal{M} $$ -theory uplift of the type IIB dual of large-N thermal QCD at low temperatures, can be consistently set to be vanishingly small.