D1 and D5-brane giant gravitons on $AdS_3 \times S^3 \times S^3 \times S^1$

Understand

We construct various examples of 1/4-BPS giant gravitons embedded into the type IIB supergravity background $AdS_{3} \times S^{3}_{+} \times S^{3}_{-} \times S^{1}$ with pure R-R flux: two D1-brane giants wrapping 1-cycles in $AdS_{3}$ and $S^{3}_{+} \times S^{3}_{-}$, and one D5-brane giant wrapping a 4-cycle in $S^{3}_{+} \times S^{3}_{-}$ and the $S^{1}$.

• These D-branes are supported by angular momenta $\alpha$ P on one 3-sphere and $(1-\alpha)$ P on the other.
• We then construct a general class of 1/8-BPS D5-brane giant gravitons wrapping 4-cycles $\Sigma$ in $S^{3}_{+} \times S^{3}_{-}$ and the $S^{1}$.
• Here $\Sigma$ is the intersection of a holomorphic surface $\mathcal{C}$ in $\mathbb{C}^{2}_{+} \times \mathbb{C}^{2}_{-}$ with the $S^{3}_{+} \times S^{3}_{-}$ submanifold.