1/N^2 corrections to the holographic Weyl anomaly

TL;DR

This work computes the subleading holographic Weyl anomaly $c-a$ for IIB supergravity on $AdS_5\times S^5/\mathbb{Z}_n$ and $AdS_5\times T^{1,1}/\mathbb{Z}_n$ by summing the contributions of shortened KK multiplets in the bulk one-loop effective action. The authors find exact agreement with the corresponding four-dimensional CFT results: for $S^5/\mathbb{Z}_n$, $c-a=0$ ($n=1$), $c-a=1/12$ ($n=2$), and $c-a=n/16$ ($n\ge3$); and for $T^{1,1}/\mathbb{Z}_n$, $c-a=n/8$, provided massive-string-loop corrections are absent or properly accounted for. A crucial aspect is the need to include twisted-sector states for even $\mathbb{Z}_n$ orbifolds of $S^5$, and the use of a regulator (via a $z^p$ weight) for the infinite KK sum, with poles discarded to extract finite results. The paper also highlights regulator sensitivities and unresolved issues related to alternative quantization and potential massive-string-loop contributions, suggesting avenues for further exploration in broader Sasaki–Einstein compactifications.

Abstract

We compute the O(1) contribution to holographic c-a for IIB supergravity on AdS_5 x S^5/Z_n and on AdS_5 x T^{1,1}/Z_n. In both cases, we find agreement with the dual field theory results, thus providing 1/N^2 checks of AdS/CFT with reduced supersymmetry. Since the holographic computation involves a sum over shortened multiplets in the KK tower, we provide some details on the S^5 and T^{1,1} spectra in a form that is convenient when considering their Z_n orbifolds. The computation for the even Z_n orbifolds of S^5 includes a sum over the multiplets in the twisted sector that is essential for obtaining agreement with the dual field theory.

Figures (2)

• Figure 1: Two of the orbifold quivers. The $\mathbb{Z}_{2}$ orbifold is special because of the chiral multiplets in the adjoints and is shown on the left. The $\mathbb{Z}_{6}$ orbifold follows the generic pattern and is shown on the right.
• Figure 2: The quivers corresponding to $T^{1,1}/\mathbb{Z}_{2}$ (on the left) and $T^{1,1}/\mathbb{Z}_{4}$ (on the right). The latter is an example of typical quivers corresponding to orbifolds of $T^{1,1}$.