The warped, resolved, deformed conifold gets flavoured

TL;DR

The authors develop a rotation-based solution-generating technique for Type IIB $SU(3)$-structure backgrounds and apply it to a seed involving D5 branes wrapped on the resolved conifold with smeared flavours. The resulting flavoured warped geometry generalizes the known flavoured KS-type backgrounds, introducing D5 and D3 sources and revealing a rich field-theory interpretation in terms of Higgsing and Seiberg dual cascades, with two competing pictures for flavours (explicit vs emergent). They analyze IR singularities, UV asymptotics, and a special $oldsymbol{Z}_2$ structure, offering a framework to relate gravity solutions to mesonic/baryonic branches and to discuss potential resolutions via flavor profiles. The work provides a bridge between geometric rotation techniques and gauge/gravity duals, highlighting practical avenues to model strongly coupled dynamics with back-reacted flavors, while leaving open questions about non-singular completions and precise IR/UV field theory identifications.

Abstract

We discuss a simple transformation that allows to generate SU(3) structure solutions of Type IIB supergravity with RR fluxes, starting from non-Kahler solutions of Type I supergravity. The method may be applied also in the presence of supersymmetric source branes. We apply this transformation to a solution describing fivebranes wrapped on the two-sphere of the resolved conifold with additional flavour fivebrane sources. The resulting solution is a generalisation of the resolved deformed conifold solution of Butti et al. by the addition of D5 brane and D3 brane sources. We propose that this solution may be interpreted in terms of a combined effect of Higgsing and cascade of Seiberg dualities in the dual field theory.

Figures (6)

• Figure 1: Plot of the function $P(\rho)$ and the dilaton for the numerical solution interpolating between the two asymptotic behaviours in (\ref{['new-solution-asymptotics']}). The plots correspond to the values $\widetilde{N}_c=10$, $\widetilde{N}_f=20$, $c=30$, and $h_1=100$.
• Figure 2: In these plots we plot the same numerical solution as in Fig. \ref{['plots-flavored']}, but we zoom in on the IR region (left) and on the UV region (right) and we compare the numerical solution (black) with the corresponding asymptotic solutions given in (\ref{['new-solution-asymptotics']}). These are plotted in red (IR solution) and in blue (UV solution).
• Figure 5: On the left: plots of $P(\rho)$ for fixed values $c=30$, $\widetilde{N}_c=10$ and different values of $\widetilde{N}_f$ (and $h_1$). The continuous curve is $\widetilde{N}_f=0$. Superimposed on this are the curves for the following values: $\widetilde{N}_f=5$ (dotted green), $\widetilde{N}_f=10$ (dotted red), $\widetilde{N}_f=20$, (dotted blue), $\widetilde{N}_f=40$ (dotted black). On the right: different plots of $\hat{h}(\rho)$ for the same values of $\widetilde{N}_f$.
• Figure 6: A Klebanov-Strassler quiver, flavoured by the addition of $N_f$ quarks.
• Figure 7: Plot of the effective resolution parameter $\alpha^2_{eff}$ as a function of $N_f$ at fixed $\nu$ and (large) $\rho$. The two branches are exchanged by a $\mathbb{Z}_2$ reflection. At $N_f=0$ the $\mathbb{Z}_2$ symmetry ${\cal I}$ is restored. At $N_f=2N_c$ the reflection symmetry ${\cal R}$ is restored.