Towards a holographic dual of large-N_c QCD

TL;DR

This work builds a holographic dual of a QCD-like theory by embedding N_f D6-branes in the D4-soliton background, in the probe limit. It demonstrates spontaneous chiral symmetry breaking for N_f=1 with m_q=0, realizes a Goldstone-like pseudoscalar, and derives a GMOR relation within the holographic setup; for N_f>1 it implements a holographic Vafa–Witten constraint preventing flavor-symmetry breaking, while predicting N_f^2 light pseudoscalars at m_q=0. At finite temperature, the model exhibits a confinement/deconfinement transition and a temperature-driven quark-sector transition, revealing a rich phase structure dependent on m_q and the SUSY-breaking scale. Overall, the paper connects string-theoretic embeddings to QCD-like phenomena, highlighting decoupling issues, the role of higher-dimensional invariances, and prospects for refining holographic approaches to low-energy QCD.

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} ψ> \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} ψ> / \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.