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 S5. 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 qN , and leave the sub-leading corrections starting at qkN (k ≥ 2) as a task for the future. We find complete agreement for the leading corrections in all examples.
Highlights
An N = 1 gauge theory is realized on the worldvolume of N D3-branes put at the apex of a Calabi-Yau cone X
We investigate the AdS/CFT correspondence for quiver gauge theories realized on D3-branes put on abelian orbifolds by using the superconformal index
We investigated the finite N corrections to the superconformal index for quiver gauge theories realized on D3-branes put in abelian orbifolds X = C3/Γ
Summary
In N = 4 SO(2N ) SYM the Pfaffian operators with dimension N correspond not to Kaluza-Klein modes of supergravity fields but to D3-branes wrapped around topologically non-trivial cycles in S5/Z2 [11]. On the gauge theory side this is because single trace operators with the length L > N are not independent but decomposable into shorter single-trace operators We can explain this on the gravity side by assuming that the operators correspond not to point-like gravitons but to giant gravitons: D3-branes wrapped on topologically trivial three-cycles in S5.
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