Towards a holographic dual of large- N c QCD

We study N f D6-brane probes in the supergravity background dual to N c D4-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 N c colours and N f 0, obeying the Gell-Mann-Oakes-Renner relation: M π 2 = −m q ψ/fπ2 . In the case 1$> N f>1 we provide a holographic version of the Vafa-Witten theorem, which states that the U(N f) flavour symmetry cannot be spontaneously broken. Further, we find N f 2−1 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.