Gauge theories on hyperbolic spaces and dual wormhole instabilities
Alex Buchel
TL;DR
This work probes holographic duals of four-dimensional gauge theories on negatively curved, compact spaces by analyzing Euclidean wormholes in type IIB supergravity. It shows that D3–anti-D3 pair production in the background four-form potential induces Schwinger-like nonperturbative instabilities that are not cured by finite temperature alone, and in many setups the wormholes acquire naked singularities before stabilization. By formulating a general probe-brane framework in warped flux backgrounds, the authors derive a universal effective potential and reveal a radion (inflaton) mass formula $m_{\text{rad}}^2 = \tfrac{2}{3}\Lambda + m^2_{\text{fluxes}} \pm m^2_{\text{geometry}}$, illustrating how fluxes can lift tachyonic directions while geometry can stabilize or destabilize depending on the deformation. They apply this to mass-deformed ${\cal N}=4$ and KS backgrounds, finding that fermionic masses raise the radion mass and can suppress instabilities in some cases, but in the ${\cal N}=2^*$ PW flow on $\Sigma_4$ a naked singularity arises before complete stabilization, implying that fully stable, single-boundary wormholes may be challenging to realize. These results clarify the nonperturbative stability constraints for holographic duals of gauge theories on negatively curved spaces and have implications for brane inflation scenarios in warped throats. The study highlights a delicate balance between flux-induced masses and geometric deformations in determining the viability of wormhole solutions and their gauge-theory interpretations.
Abstract
We study supergravity duals of strongly coupled four dimensional gauge theories formulated on compact quotients of hyperbolic spaces. The resulting background geometries are represented by Euclidean wormholes, which complicates establishing the precise gauge theory/string theory correspondence dictionary. These backgrounds suffer from the non-perturbative instabilities arising from the D3 - anti-D3 pair production in the background four-form potential. We discuss conditions for suppressing this Schwinger-like instability. We find that Euclidean wormholes arising in this construction develop a naked singularity, before they can be stabilized.