Flavoring the gravity dual of N=1 Yang-Mills with probes

TL;DR

The paper addresses embedding D5-brane probes in the gravity dual of $N=1$ SYM and using these probes to introduce fundamental flavors. It employs kappa symmetry to derive SUSY-preserving embeddings, uncovering a rich set of abelian and non-abelian worldvolume solitons (including unit-winding and zero-winding configurations) and analyzing their energy bounds. By studying quadratic fluctuations around the unit-winding embedding, it derives a discrete meson spectrum for $N=1$ SQCD with a small number of flavors, organized by quantum numbers and mass scales, and reveals a degeneracy between scalar and vector mesons along with R-symmetry breaking patterns that align with field theory expectations. The results provide a concrete holographic realization of mesons in a confining, chiral-symmetry-breaking background and suggest avenues for extending the analysis to KS-like geometries and beyond the quenched approximation.

Abstract

We study two related problems in the context of a supergravity dual to N=1 SYM. One of the problems is finding kappa symmetric D5-brane probes in this particular background. The other is the use of these probes to add flavors to the gauge theory. We find a rich and mathematically appealing structure of the supersymmetric embeddings of a D5-brane probe in this background. Besides, we compute the mass spectrum of the low energy excitations of N=1 SQCD (mesons) and match our results with some field theory aspects known from the study of supersymmetric gauge theories with a small number of flavors.

Figures (7)

• Figure 1: Curves $y=y(x)$ for three values of the winding number $n$: $n=0$ (solid line), $n=1$ (dashed curve) and $n=2$ (dotted line). These three curves correspond to $r_*=1$.
• Figure 2: Comparison between the non-abelian (solid line) and abelian (dashed line) unit-winding embeddings for the same value of $r_*$ . The non-abelian embedding is the one corresponding to eq. (\ref{['noabflavor']}) and the abelian one is that given in eq. (\ref{['abspikes']}) for $n=1$ and $c=1$. The curves for two different values of $r_*$ ($r_*=0.5$ and $r_*=1$) are shown. The variables $(x,y)$ are the ones defined in eq. (\ref{['cartesian']}).
• Figure 3: Graphic representation of the unit winding embedding of eq. (\ref{['nabcosh']}) for three values of the constant $C$: $C=0.5$ (dashed line), $C=1$ (solid line) and $C=1.5$ (dotted line). The variables $(x,y)$ are the ones defined in eq. (\ref{['cartesian']}).
• Figure 4: Graphic representation of the first three fluctuation modes for $r_*=0.3$, $\Lambda=3$ and $l=0$. The three curves have been normalized to have $\xi(r_*)=1$.
• Figure 5: Plot of $\delta y\equiv\zeta\sin\theta$ versus $x= r\cos\theta$ for the first four modes for $r_*=0.3$, $\Lambda=3$ and $l=0$. The dashed and dotted curves pass through the origin and correspond to the first two modes of figure 3.