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Holographic Techni-dilaton

Techni-dilaton, a pseudo-Nambu-Goldstone boson of scale symmetry, was predicted long ago in the Scale-invariant/Walking/Conformal Technicolor (SWC-TC) as a remnant of the (approximate) scale symmetry associated with the conformal fixed point, based on the conformal gauge dynamics of ladder Schwinger-Dyson (SD) equation with non-running coupling. We study the techni-dilaton as a flavor-singlet bound state of techni-fermions by including the techni-gluon condensate (tGC) effect into the previous (bottom-up) holographic approach to the SWC-TC, a deformation of the holographic QCD with $γ_m \simeq 0$ by large anomalous dimension $γ_m \simeq 1$. With including a bulk scalar field corresponding to the gluon condensate, we first improve the Operator Product Expansion of the current correlators so as to reproduce gluonic $1/Q^4$ term both in QCD and SWC-TC. We find in QCD about $10\%$ (negative) contribution of gluon condensate to the $ρ$ meson mass. We also calculate the oblique electroweak $S$-parameter in the presence of the effect of the tGC and find that for the fixed value of $S$ the tGC effects dramatically reduce the flavor-singlet scalar (techni-dilaton) mass $M_{\rm TD}$ (in the