Abstract
Abstract The superconformal index of quiver gauge theories realized on D3-branes in toric Calabi–Yau cones is investigated. We use the AdS/CFT correspondence and study D3-branes wrapped on supersymmetric cycles. We focus on brane configurations in which a single D3-brane is wrapped on a cycle, and we do not take account of branes with multiple wrapping. We propose a formula that gives finite-$N$ corrections to the index caused by such brane configurations. We compare the predictions of the formula for several examples with the results on the gauge theory side obtained by using localization for small sizes of gauge groups, and confirm that the formula correctly reproduces the finite-$N$ corrections up to the expected order.
Highlights
Shows if N is small the Planck length lp becomes comparable with the AdS radius L and the quantum gravity effect is expected to be relevant
D3-branes wrapped on supersymmetric cycles in the internal space contribute to the superconformal index as a finite N correction
We calculate the superconformal index on the gravity side according to the formula (3.6) and compare the obtained results with those numerically calculated on the gauge theory side by localization method summarized in Appendix A to confirm that our prescription does work correctly
Summary
The five-dimensional Sasaki-Einstein manifold SE5 is the subset of the Calabi-Yau cone defined by ρ = 1. If I1 and I2 are two adjacent corners of the toric diagram and k := I2−I1 > 1 there are k − 1 vertices between I1 and I2, and the corresponding cycles SI are shrinking at the degenerate corners CI1+1/2 = · · · = CI2−1/2. This means the existence of Ak type singularity along the S1 fiber over the degenerate corners. Each shrinking three-cycle SI (I1 < I < I2) is the direct product of the S1 and a shrinking two-cycle at the singularity
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