Towards a holographic dual of large-NcQCD

We study N_f D6-brane probes in the supergravity background dual to N_cD4-branes compactified on a circle with supersymmetry-breaking boundaryconditions. In the limit in which the resulting Kaluza--Klein modes decouple,the gauge theory reduces to non-supersymmetric, four-dimensional QCD with N_ccolours and N_f << N_c flavours. As expected, this decoupling is not fullyrealised within the supergravity/Born--Infeld approximation. For N_f = 1 andmassless quarks, m_q = 0, we exhibit spontaneous chiral symmetry breaking by aquark condensate, <\bar{psi} \psi> \neq 0, and find the associated massless`pion' in the spectrum. The latter becomes massive for m_q > 0, obeying theGell-Mann--Oakes--Renner relation: M_pi^2= - m_q <\bar{psi} \psi> / \f_pi^2. Inthe case 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 thespectrum. We argue that these are not (pseudo) Goldstone bosons and speculateon the string mechanism responsible for their lightness. We then study thetheory at finite temperature and exhibit a phase transition associated with adiscontinuity in the chiral condensate. D6/anti-D6 pairs are also brieflydiscussed.Comment: 43 pages, LaTeX; v3: Scalar vs. pseudo-scalar nature of mesons clarified, references added. v4: Small change in Acknowledgment