Analytic continuation and the giant graviton expansion

There is now strong evidence that the superconformal index of holographic gauge theories admits a giant graviton expansion capturing the worldvolume dynamics of spherical D3-branes moving in internal space. While the giant graviton indices may be written as suitable contour integrals, care must be taken in their evaluation, as there can be an ambiguity in choice of integration contour or, equivalently, “pole selection”. We resolve this ambiguity by using Murthy’s recent expansion of the superconformal index to provide a rigorous underpinning of the evaluation of the supergravity giant graviton indices. In doing so, we directly relate Murthy’s giant graviton expansion to the supergravity D3-brane expansion.