Gravity Duals of Fractional Branes in Various Dimensions

TL;DR

This work constructs gravity duals for space-filling regular and fractional Dp-branes on conical transverse spaces, with fractional branes realized as wrapped D(p+2) branes on harmonic 2-cycles and, in M-theory, wrapped M5 branes on harmonic 3-cycles. It derives explicit warp-factor solutions for Type II theories across multiple p, analyzes their UV and IR behavior, and discusses gauge-theory interpretations including cascades, confinement, and Higgsing, linking to KT/KS-type physics. The eleven-dimensional analysis extends to regular and fractional M2-branes with logarithmic RG flow induced by wrapped M5s, while the D-strings and higher-dimensional examples reveal rich duals with varying numbers of colors $N_{\rm eff}(r)$ and potential RS-like IR completions. The results situate these gravity solutions within the Cveti\v{c}-L\"u-Gibbons-Pope ansatz, highlighting UV perturbations by harmonic forms $\omega_2$, $\omega_3$, or $\omega_4$ as dual to relevant operators in the boundary theories and broadening the landscape of holographic duals with less-than-maximal supersymmetry.

Abstract

We derive type II supergravity solutions corresponding to space-filling regular and fractional Dp branes on (9-p)-dimensional conical transverse spaces. Fractional Dp-branes are wrapped D(p+2)-branes; therefore, our solutions exist only if the base of the cone has a non-vanishing Betti number b_2. We also consider 11-dimensional SUGRA solutions corresponding to regular and fractional M2 branes on 8-dimensional cones whose base has a non-vanishing b_3. (In this case a fractional M2-brane is an M5-brane wrapped over a 3-cycle.) We discuss the gauge theory intepretation of these solutions, as well as of the solutions constructed by Cvetic et al. in hep-th/0011023 and hep-th/0012011.