Nonperturbative Instability of AdS_5 x S^5/Z_k

TL;DR

This paper proves that $AdS_{5} \times S^{5}/\mathbb{Z}_{k}$ with a freely acting orbifold ($k>3$) suffers a nonperturbative decay analogous to the Kaluza-Klein bubble of nothing, despite the absence of perturbative tachyons at large $\lambda$. It constructs both smeared and localized bubble solutions, showing that the smeared case necessarily involves a smeared D3-brane instanton to satisfy flux constraints, and develops large-$k$ analytic approximations plus numerical results that confirm the existence of a decay channel for $k>3$ (with $k=3$ special due to supersymmetry). The decay rate diverges in the UV, implying the dual gauge theory is only well-defined as an effective theory with UV/IR cutoffs, and the symmetry-breaking pattern at strong coupling mirrors, in spirit, weak-coupling expectations via twisted-trace operator condensates. The work thus links nonperturbative bulk instabilities to operator dynamics in the dual CFT and suggests broader implications for the stability of nonconformal and conifold-related AdS/CFT setups.

Abstract

We study the AdS/CFT correspondence with boundary conditions AdS_5 x S^5/Z_k, where the Z_k acts freely but breaks all supersymmetry. While there are closed string tachyons at small 't Hooft coupling, there are no tachyons at large coupling. Nevertheless, we show that there is a nonperturbative instability directly analogous to the decay of the Kaluza-Klein vacuum. We discuss the implications of this instability for the strongly coupled dual field theory, and compare with earlier studies of this theory at weak coupling.

Figures (1)

• Figure 1: $g_{\chi \chi}$ for the $k = 10$ bounce (dashed line) and the asymptotic form (solid line).