Chiral Symmetry Breaking and Pions in Non-Supersymmetric Gauge/Gravity Duals

TL;DR

This work demonstrates that gravity duals of large-$N$ non-supersymmetric gauge theories with fundamental matter, realized via D7-brane probes in deformed AdS backgrounds, can dynamically generate quark condensates and break chiral symmetry. By analyzing D7 embeddings in both the AdS-Schwarzschild and Constable-Myers geometries, the authors find a quark condensate only for nonzero quark mass in the finite-temperature AdS-Schwarzschild case and a spontaneous chiral condensate with a Goldstone mode in the Constable-Myers background, where the condensate also prevents the D7-brane from reaching the IR singularity. The meson spectra in both backgrounds display a mass gap, with the AdS-Schwarzschild case showing a spectrum tied to the temperature scale and the Constable-Myers case yielding a massless mode at $m\to 0$ and a pion-like spectrum for small masses. Collectively, these results illustrate how non-supersymmetric holographic setups can capture qualitative aspects of chiral dynamics and provide a controlled setting to study light mesons and their interactions in a strongly coupled gauge theory context.

Abstract

We study gravity duals of large N non-supersymmetric gauge theories with matter in the fundamental representation by introducing a D7-brane probe into deformed AdS backgrounds. In particular, we consider a D7-brane probe in both the AdS Schwarzschild black hole solution and in the background found by Constable and Myers, which involves a non-constant dilaton and S^5 radius. Both these backgrounds exhibit confinement of fundamental matter and a discrete glueball and meson spectrum. We numerically compute the quark condensate and meson spectrum associated with these backgrounds. In the AdS-black hole background, a quark-bilinear condensate develops only at non-zero quark mass. We speculate on the existence of a third order phase transition at a critical quark mass where the D7 embedding undergoes a geometric transition. In the Constable-Myers background, we find a chiral symmetry breaking condensate as well as the associated Goldstone boson in the limit of small quark mass. The existence of the condensate ensures that the D7-brane never reaches the naked singularity at the origin of the deformed AdS space.

Figures (14)

• Figure 1: The D7 embedding in $AdS_5 \times S^5$.
• Figure 2: - numerical solutions of EoM in AdS showing that in the presence of a condensate asymptotically the solutions are divergent. The regular solution is the mass only solution.
• Figure 3: - numerical solutions of the meson EoM for different values of $M$ showing the identification of the first bound state mass - the exact regular solution is plotted between the two numerical flows.
• Figure 4: Different possibilities for solutions of the D7-brane equations of motion. The semicircles are lines of constant $r$, which should be interpreted as a scale in the dual Yang-Mills theory. The curves of type $A,B$ have an interpretations as an RG flow, while the curve $C$ does not.
• Figure 5: An example (for $m=0.6$) of the different flow behaviours around the regular (physical) solution.