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} (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.
Highlights
Dedicated by one of the authors (AM) to the memory of his supervisor, the late Professor Daniel Koltun who introduced him to χPT 25 years ago — a subject the former has returned back to after 22 years — and instilled in the former the importance of uncompromising independence of thought and inquiry
We take the first step in this direction by obtaining the values of the coupling constants of the O(p4) χPT Lagrangian in the chiral limit involving the NGBs and ρ meson from the M-theory/type IIA dual of large-N thermal QCD, inclusive of the O(R4) corrections
Sakai Sugimoto model reproduces various physical quantities of low energy QCD but this model deviates from realistic QCD above the energy scale of the vector mesons because they obtain a fourdimensional theory by compactifying D4-branes on a circle of radius MK−K1 with an infinite tower of Kaluza-Klein modes of mass scale MKK arises
Summary
-corrections of the M-theory uplift of holographic thermal QCD of [14] as worked out in [15, 19] in conjunction with the O(R4)-corrections to the same as worked out in [16], can be used to match the experimental values of the coupling constants up to O(p4) appearing in the SU(3) Chiral Perturbation theory Lagrangian for the pion and rho vector mesons as well as their flavor partners, in the chiral limit. In working in the ψ = 0, 2π, 4π patches close to the type IIB Ouyang embedding effected by working near small θ1,2 the aforementioned combination is Cz(1z) − 2Cθ(11z) + 2Cθ(11x) , where CM(1)N s are the constants of integration appearing in the solutions to the EOMs for the O(R4)-corrections GM MN,(1) = GM MN,(0) (1 + fMN ), being the MQGP metric of [14, 19] This dependence is expected to change in the ψ = 2nπ, n = 0, 1, 2-. Upon matching with the experimental value of the one-loop renormalized Lr10, one obtains a non-linear relation between the constants of integration appearing in the radial profile functions for the π and ρ mesons in the IR, as well as the coefficient of the term required to exist resolution-parameter-IR-cut-off relation (discussed in the second bullet above) upon matching with the experimental values of Lr1,2,3.
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