Finite $N$ corrections to the superconformal index of orbifold quiver gauge theories

Abstract

We investigate the AdS/CFT correspondence for quiver gauge theories realized on D3-branes put on abelian orbifolds by using the superconformal index. We assume that on the gravity side the finite $N$ corrections of the index are reproduced by D3-branes wrapped on three particular three-cycles in the internal space $\mathcal{Y}$, the abelian orbifold of ${\mathbf{S}}^5$. We first establish the relation between baryonic charges on the gauge theory side and the D3-brane wrapping numbers and holonomies on D3-branes. Then we confirm our proposal by comparing the results of localization for gauge theories and the results on the AdS side including the contributions of D3-branes and excitation on them for many examples. We only focus on the leading finite $N$ corrections starting from $q^N$, and leave the sub-leading corrections starting at $q^{kN}$ ($k\ge 2$) as a task for the future. We find complete agreement for the leading corrections in all examples.

arXiv comment53 pages, 9 figures, v2:minor changes, references added

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• Higher-derivative corrections to flavoured BPS black hole thermodynamics and holography
• Flavor symmetries of six-dimensional $\mathcal{N}=(1,0)$ theories from AdS/CFT correspondence
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