Index for Orbifold Quiver Gauge Theories
Yu Nakayama
TL;DR
The paper studies the protected index of four-dimensional SCFTs from D-branes at $\mathbb{C}^3/\Gamma$, comparing gauge-theory and gravity computations to test AdS/CFT. It computes the index in the free gauge theory limit using a unitary matrix-model approach and derives explicit product formulas for $Z_k\subset SU(3)$ and $Z_k\subset SU(2)$ orbifolds, after removing decoupled $U(1)$ factors. It then evaluates the type IIB supergravity index on $AdS_5 \times S^5/\Gamma$ by projecting to $\Gamma$-invariants and exponentiating single-particle contributions, finding agreement in the untwisted sector and identifying the need for twisted-sector corrections when fixed loci exist. The results provide a concrete consistency check of AdS/CFT for orbifold/quiver theories and motivate extensions to Sasaki–Einstein backgrounds and a more detailed understanding of twisted-sector spectra.
Abstract
We compute the index for orbifold quiver gauge theories. We compare it with the results obtained from the type IIB supergravity (superstring) on AdS_5 \times S^5/Γ.