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

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 $\mathcal{M}$-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 $\mathcal{O}(p^4)$ $\chi$PT Lagrangian in the chiral limit involving the NGBs and $\rho$ meson (and its flavor partners) from the $\mathcal{M}$-theory /type IIA dual of large-$N$ thermal QCD, inclusive of the $\mathcal{O}(R^4)$ 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 $\mathcal{O}(R^4)$ 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 $\mathcal{O}(R^4)$ corrections in the UV to the $\mathcal{M}$-theory uplift of the type IIB dual of large-$N$ thermal QCD, can be consistently set to be vanishingly small.

arXiv commentv2: 1+51 pages, LaTeX; Added refs and explanatory text- an app summarizing the HLS formalism (based on Harada and Yamawaki's Phys Rep review), an app on O(R^4) corrections in the D6-brane DBI action, a small discussion on holographic renormalization and a summary of results and a table (fitting the model-related parameters to phenomenological values of O(p^4) ChPT LECs); to appear in JHEP

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• Phases of a 10-D Holographic hard wall model