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. The holomorphic surface $\mathcal{ C}$ is defined by $f(y_{ 1}z_{ 1},y_{ 1}z_{ 2},y_{ 2}z_{ 1},y_{ 2}z_{ 2}) = 0$, with $y_{ a}$ and $z_{ a}$ the $\mathbb{ C}^{ 2}_{ \pm}$ complex coordinates. There is supersymmetry enhancement to 1/4-BPS in the special case $f(y_{ 1}z_{ 1}) = 0$ of which our original D5-brane giant graviton is an example.
Categories: hep-th