Towards a holographic dual of large-NcQCD

Abstract

We study NfD6-brane probes in the supergravity background dual to NcD4-branes compactified on a circle with supersymmetry-breaking boundary conditions. In the limit in which the resulting Kaluza-Klein modes decouple, the gauge theory reduces to non-supersymmetric, four-dimensional QCD with Nc colours and Nf << Ncflavours. As expected, this decoupling is not fully realised within the supergravity/Born-Infeld approximation. For Nf = 1 and massless quarks, mq = 0, we exhibit spontaneous chiral symmetry breaking by a quark condensate, ⟨ψ⟩≠0, and find the associated massless `pion' in the spectrum. The latter becomes massive for mq > 0, obeying the Gell-Mann-Oakes-Renner relation: Mπ2 = −mq ⟨ψ⟩/fπ2. In the case Nf>1 we provide a holographic version of the Vafa-Witten theorem, which states that the U(Nf) flavour symmetry cannot be spontaneously broken. Further, we find Nf2−1 unexpectedly light pseudo-scalar mesons in the spectrum. We argue that these are not (pseudo-)Goldstone bosons and speculate on the string mechanism responsible for their lightness. We then study the theory at finite temperature and exhibit a phase transition associated with a discontinuity in ⟨ψ⟩(T). D6/ pairs are also briefly discussed.