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This paper continues the investigation of the modified Sakai-Sugimoto modelproposed in arXiv:0708.3233. Here we discuss in detail numerical solutions tothe classical equations for the brane profile and the tachyon condensate. Anultraviolet cut-off turns out to be essential because the numerical solutionstend to rapidly diverge from the desired asymptotic solutions, beyond asufficiently large value of the holographic coordinate. The required cut-off isdetermined by the non-normalizable part of the tachyon and is parametricallyfar smaller than that dictated by consistency of a description in terms of10-dimensional bulk gravity. In arXiv:0708.3233 we had argued that the solutionin which the tachyon field goes to infinity at the point where the brane andantibrane meet has only one free parameter, which may be taken to be theasymptotic brane-antibrane separation. Here we present numerical evidence infavour of this observation. We also present evidence that the non-normalizablepart of the asymptotic tachyon solution, which is identified with quark mass inthe QCD-like boundary theory, is determined by this parameter. We show that thenormalizable part of the asymptotic tachyon solution determines the quarkcondensate, but this requires holographic renormalization of the on-shellboundary brane action because of the presence of infinite cut-off dependentterms. Our renormalization scheme gives an exponential dependence on thecut-off to the quark mass. We also discuss meson spectra in detail and showthat the pion mass is nonzero and satisfies the Gell-Mann-Oakes-Renner relationwhen a small quark mass is switched on.

Tachyon condensation and quark mass in modified Sakai-Sugimoto model