Towards a holographic dual of large-Nc QCD

Abstract

We study Nf D6-brane probes in the supergravity background dual to Nc 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 Nc colours and Nf ≪ Nc flavours. 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, 〈ψ̄psi; 〉 ≠ 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 = -m q〈ψ̄psi; 〉/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 〈ψ̄psi; 〉(T). D6/D6 pairs are also briefly discussed. © SISSA/ISAS 2004.