Towards a holographic dual of large-N_c QCD

TL;DR

This paper develops a holographic model of large-N_c QCD using D-brane probes, demonstrating chiral symmetry breaking, meson spectra, and phase transitions at finite temperature within a supergravity framework.

Contribution

It introduces a holographic dual of large-N_c QCD with chiral symmetry breaking and meson spectra, extending the gauge/gravity correspondence to non-supersymmetric QCD-like theories.

Findings

Demonstrates spontaneous chiral symmetry breaking with a quark condensate.

Derives the Gell-Mann--Oakes--Renner relation for meson masses.

Identifies a finite temperature phase transition related to the chiral condensate.

Abstract

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 << N_c flavours. As expected, this decoupling is not fully realised within the supergravity/Born--Infeld approximation. For N_f = 1 and massless quarks, m_q = 0, we exhibit spontaneous chiral symmetry breaking by a quark condensate, <\bar{psi} \psi> \neq 0, and find the associated massless `pion' in the spectrum. The latter becomes massive for m_q > 0, obeying the Gell-Mann--Oakes--Renner relation: M_pi^2= - m_q <\bar{psi} \psi> / \f_pi^2. In the 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 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 the chiral condensate. D6/anti-D6 pairs are also briefly discussed.