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The spectrum of IIB supergravity on AdS_5 x S^5/Z_3 and a 1/N^2 test of AdS/CFT

Arash Arabi Ardehali, James T. Liu, Phillip Szepietowski

TL;DR

This work tests AdS/CFT beyond leading order by deriving the full KK spectrum of IIB supergravity on $AdS_5\times S^5/\mathbb Z_3$ and organizing it into $\mathcal N=2$ multiplets. Using the one-loop holographic Weyl anomaly framework, the authors sum over shortened KK states to compute the subleading $c-a$ and show it equals $\frac{3}{16}$, matching the dual $\mathrm{SU}(N)^3$ quiver gauge theory. The analysis highlights the role of multiplet shortening and provides a precise operator dictionary between bulk KK modes and protected boundary operators. This confirms the stability of AdS/CFT predictions at subleading order for orbifold backgrounds and motivates analogous checks in other Sasaki–Einstein compactifications such as $T^{1,1}$.

Abstract

We present the complete Kaluza-Klein spectrum resulting from the compactification of IIB supergravity on S^5/Z_3. Knowledge of this spectrum allows us to perform a holographic computation of the difference of central charges c-a of the dual SU(N)^3 quiver gauge theory. We find the numerical value c-a=3/16, in exact agreement with the field theory result.

The spectrum of IIB supergravity on AdS_5 x S^5/Z_3 and a 1/N^2 test of AdS/CFT

TL;DR

This work tests AdS/CFT beyond leading order by deriving the full KK spectrum of IIB supergravity on and organizing it into multiplets. Using the one-loop holographic Weyl anomaly framework, the authors sum over shortened KK states to compute the subleading and show it equals , matching the dual quiver gauge theory. The analysis highlights the role of multiplet shortening and provides a precise operator dictionary between bulk KK modes and protected boundary operators. This confirms the stability of AdS/CFT predictions at subleading order for orbifold backgrounds and motivates analogous checks in other Sasaki–Einstein compactifications such as .

Abstract

We present the complete Kaluza-Klein spectrum resulting from the compactification of IIB supergravity on S^5/Z_3. Knowledge of this spectrum allows us to perform a holographic computation of the difference of central charges c-a of the dual SU(N)^3 quiver gauge theory. We find the numerical value c-a=3/16, in exact agreement with the field theory result.

Paper Structure

This paper contains 10 sections, 39 equations, 12 tables.

Table of Contents

  1. Introduction
  2. The Kaluza-Klein spectrum of IIB supergravity on $\mathrm{AdS}_5\times S^5/\mathbb Z_3$
  3. The $S^5/\mathbb Z_3$ orbifold
  4. Filling out $\mathcal{N}=2$ supermultiplets
  5. Multiplet shortening
  6. Dual operators with protected dimension
  7. The holographic computation of $c-a$
  8. Discussion
  9. The branching rules for $\mathrm{SU}_{4}\supset \mathrm{SU}_{3}\times \mathrm U_{1}$ and projection onto $\mathbb Z_3$ singlets
  10. $\mathcal{N}=2$ multiplet structure