Finite N corrections to the superconformal index from D3-brane analysis in AdS_5/CFT_4

In the context of the AdS/CFT, the Type IIB superstring theory on AdS_5 \times SE_5 corresponds to an N=1 quiver gauge theory, where SE_5 is a five-dimensional Sasaki-Einstein manifold. We study this correspondence by using the superconformal index, which contains the information of the BPS spectrum in the theory. It is known that the index of the large N limit is evaluated by the Kaluza-Klein modes on SE_5 and the agreement with CFT results was confirmed in many examples. In this talk, we consider the finite N corrections to the index on the gravity side as a next step. To do this, we focus on a single D3-brane wrapped around a three-cycle on SE_5. Because there are in general several three-cycles on SE_5, we need to sum up contributions of these single D3-branes. By using the D3-brane analysis, we propose a prescription to calculate the finite N corrections to the index. We explain our prescription through some examples and see the agreement with the CFT results calculated by the localization method.