Simple-Sum Giant Graviton Expansions for Orbifolds and Orientifolds
Shota Fujiwara, Yosuke Imamura, Tatsuya Mori, Shuichi Murayama, Daisuke Yokoyama
Abstract
Abstract We study giant graviton expansions of the superconformal index of 4D orbifold/orientifold theories. In general, a giant graviton expansion is given as a multiple sum over wrapping numbers. It is known that the expansion can be reduced to a simple sum for the ${\cal N}=4$ U(N) supersymmetric Yang–Mills (SYM) by choosing appropriate expansion variables. We find such a reduction occurs for a few examples of orbifold and orientifold theories: the $\mathbb {Z}_k$ orbifold and orientifolds with O3 and O7. We also argue that for a quiver gauge theory associated with a toric Calabi–Yau 3-fold the simple-sum expansion works only if the toric diagram is a triangle, i.e. the Calabi–Yau is an orbifold of $\mathbb {C}^3$.