Chiral Dynamics From AdS Space

TL;DR

We address how chiral symmetry breaking and the resulting pion dynamics can be realized in a gravity dual using a probe D7 brane in the non-supersymmetric Constable–Myers geometry. The authors derive a non-linear chiral Lagrangian from fluctuations of the D7-brane, numerically extract the quark condensate $⟨\bar{q}q⟩$, the pion decay constant $f_π$, and higher-order coefficients $L_i$, and study vector mesons under weak gauging. The results show the pions are genuine Goldstone modes with $M_π^2 = 4 ν^3 m / f_π^2$ in the small-mass limit and that the low-energy constants scale in line with naive dimensional analysis, with the non-Abelian extension yielding consistent $f_π$ and Goldstone-like interactions. Vector meson dynamics are analyzed via the worldvolume gauge field, revealing a spectrum in qualitative agreement with AdS expectations while highlighting limitations in accessing axial sectors. Overall, the work provides a concrete holographic realization of chiral dynamics in a QCD-like setting and delivers quantitative predictions for low-energy constants and vector-meson structure in a strongly coupled regime.

Abstract

We study the low energy dynamics of pions in a gravity dual of chiral symmetry breaking. The string theory construction consists of a probe D7 brane in the Constable Myers non-supersymmetric background, which has been shown to describe chiral symmetry breaking in the pattern of QCD. We expand the D7 brane's Dirac Born Infeld action for fluctuations that correspond to the Goldstone mode and show that they take the form of a non-linear chiral lagrangian. We numerically compute the quark condensate, pion decay constant and higher order Gasser Leutwyler coefficients. We find their form is consistent with naive dimensional analysis estimates. We also explore the gauging of the quark's chiral symmetries and the vector meson spectrum.

Figures (8)

• Figure 1: Solutions of (\ref{['eommc']}) for the position of the D7 brane showing chiral symmetry breaking in the massless limit and a sketch of the D7s position in the space.
• Figure 2: Solutions for the $w_6$ flow when $w_5=0$ showing the dependence of the condensate on the quark mass.
• Figure 3: $w_5, w_6$ flows for $m=0.1$, $\theta=90^o$ showing the possibility of a regular flow between these values of $c$.
• Figure 4: $w_6$ flows for m=0.46 with positive and negative condensate solutions
• Figure 5: Vacuum energy, with that at $m=0$ subtracted, for $\theta=0^o$ and $180^O$ showing a lower energy for the case where the mass and condensate are both positive.