Analytic continuation for giant gravitons

We investigate contributions of giant gravitons to the superconformal index. We concentrate on coincident giant gravitons wrapped around a single cycle, and each contribution is obtained by a certain variable change for fugacities from the index of the worldvolume theory on the giant gravitons. Because we treat the index as a series of fugacities and the variable change relates different convergence regions, we need an analytic continuation before summing up such contributions. We propose a systematic prescription for the continuation. Although our argument is based on some unproved assumptions, it passes non-trivial numerical checks for some examples. With the prescription we can calculate the indices of the M5-brane theories from those of the M2-brane theories, and vice versa.