(Phenomenology/Lattice-Compatible) $SU(3)$ M$\chi$PT HD up to ${\cal O}(p^4)$ and the ${\cal O}\left(R^4\right)$-Large-$N$ Connection

TL;DR

This paper derives low-energy coupling constants for QCD-like theories from M-theory, incorporating ${ m O}(R^4)$ corrections and large-$N$ effects, ensuring compatibility with experimental and lattice data.

Contribution

It provides the first calculation of ${ m O}(p^4)$ chiral perturbation theory couplings from M-theory duals, including ${ m O}(R^4)$ corrections, and establishes their relation to large-$N$ suppression.

Findings

Coupling constants match phenomenological and lattice results.

${ m O}(R^4)$ corrections can be negligible in the UV.

Higher derivative and large-$N$ suppressed corrections are related.

Abstract

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 ${\cal M}$-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 ${\cal O}(p^4)$ $\chi$PT Lagrangian in the chiral limit involving the NGBs and $\rho$ meson (and its flavor partners) from the ${\cal M}$-theory /type IIA dual of large-$N$ thermal QCD, inclusive of the ${\cal O}(R^4)$ corrections. We observe that ensuring compatibility with phenomenological/lattice results (the values ) as given in arXiv:1510.01634[hep-ph], requires a relationship relating the ${\cal O}(R^4)$ 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 ${\cal O}(R^4)$ corrections in the UV to the ${\cal M}$-theory uplift of the type IIB dual of large-$N$ thermal QCD, can be consistently set to be vanishingly small.