Various Wrapped Branes from Gauged Supergravities

TL;DR

The paper develops a unified program to construct and analyze wrapped brane configurations using maximally supersymmetric gauged supergravities. By performing twisting and domain-wall–like reductions, it yields supersymmetric wrapped D3, M2, and NS5 branes across diverse non‑compact holonomy backgrounds and provides explicit BPS equations and their solutions, including AdS backgrounds and central charges. It also explores non‑BPS AdS solutions in massive IIA/CY settings, highlighting potential dual conformal field theories and the role of singularities. The results illuminate how twisted worldvolume theories on wrapped branes realize Higgs and Coulomb branches within holographic duals and offer avenues for studying lower‑SUSY AdS/CFT with controlled gravity duals.

Abstract

We study wrapped brane configurations via possible maximally supersymmetric gauged supergravities. First, we construct various supersymmetric wrapped D3 brane configurations from D=5 N=8 SO(6) gauged supergravity. This procedure provides certain new examples of wrapped D3 branes around supersymmetric cycles inside non-compact special holonomy manifolds. We analyze their behaviors numerically in order to discuss a correspondence to Higgs and Coulomb branches of sigma models on wrapped D3 branes. We also realize supersymmetric wrapped M2 branes from D=4 N=8 SO(8) gauged supergravity. Then, we study supersymmetric wrapped type IIB NS5 branes by D=7 N=4 SO(4) gauged supergravity. We show a method to derive them by using supersymmetric wrapped M5 branes in D=7 N=4 SO(5) gauged supergravity. This method is based on a domain wall like reduction. Solutions include NS5 branes wrapped around holomorphic $CP^2$ inside non-compact Calabi-Yau threefold. Their behavior shows a similar feature to that for NS5 branes wrapped around holomorphic $CP^1$ inside non-compact $K3$ surface. This construction also provides a check of preserved supersymmetry for a solution interpreted within a string world-sheet theory introduced by Hori and Kapustin. Finally, we find new non-supersymmetric solutions including AdS space-times in D=6 N=2 $SU(2)\times U(1)$ massive gauged supergravity. These solutions can be interpreted as non-supersymmetric wrapped D4-D8 configurations which are dual to non-supersymmetric conformal field theories realized on wrapped D4 branes.

Figures (10)

• Figure 1: Behavior of $e^{f(r)},e^{g(r)}$ for wrapped D3 branes around supersymmetric $\Sigma_{g\geq 2}$ in $CY_4$. Numerical solution approaches to the AdS$_3$ solution (\ref{['2cy4ads']}) plotted by bold lines.
• Figure 2: Behavior of $e^{f(r)},e^{g(r)}$ for wrapped D3 branes on supersymmetric $CP^1$ in $CY_4$.
• Figure 3: Behavior of $e^{f(r)},e^{g(r)}$ and $e^{\phi(r)}$ for wrapped D3 branes around supersymmetric $H^3$ in $CY_3$. We denote plots of solutions with $C=0.75, 0.25$ by usual lines, a plot with $C=0.01$ by a bold line, and plots $C=-0.1, -0.5$ by dotted lines.
• Figure 4: Behavior of $e^{f(r)},e^{g(r)}$ and $e^{\phi(r)}$ for wrapped D3 branes around supersymmetric $S^3$ in $CY_3$. We denote plots of solutions with $C=0.75, 0.25$ by usual lines, a plot with $C=0$ by a bold line, and plots with $C=-0.25,-0.75$ by dotted lines.
• Figure 5: Behavior of $e^{f(r)},e^{g(r)}$ and $e^{\phi(r)}$ for wrapped D3 branes around supersymmetric $H^3$ in non-compact $G_2$ holonomy manifolds. We denote plots of solutions with $C=-1, -0.15$ by usual lines, a plot with $C=\frac{1}{32}+\frac{\log{2}}{96}$ by a bold line, and plots with $C=0.1, 0.5$ by dotted lines. Solution with $C=\frac{1}{32}+\frac{\log{2}}{96}$ approaches to the AdS$_2$ solution (\ref{['d3g2ads']}) at large $r$.