Euclidean Wormholes and Holography

TL;DR

The paper probes Euclidean AdS wormholes with two boundaries to extract holographic constraints on the dual Euclidean QFTs. By computing cross-boundary and Wilson-loop observables across Einstein–Dilaton, Einstein–Yang–Mills, and AdS$_2$ wormholes, it finds that cross-boundary correlators remain finite in the UV, suggesting UV factorization into two decoupled sectors connected by a soft non-local interaction. It further analyzes multi-trace deformations and provides a concrete field-theory analogue, arguing that the UV-soft coupling in Euclidean space can yield interesting IR dynamics without introducing short-distance singularities, while stability imposes nontrivial bounds. The results support a picture in which holographic duals consist of coupled QFTs with controlled non-local inter-boundary couplings, offering insights into the role of wormholes in quantum gravity and potential microscopic realizations such as bipartite gauge theories connected by fluxes or instantons.

Abstract

Asymptotically AdS wormhole solutions are considered in the context of holography. Correlation functions of local operators on distinct boundaries are studied. It is found that such correlators are finite at short distances. Correlation functions of non-local operators (Wilson loops) on distinct boundaries are also studied, with similar conclusions. Deformations of the theory with multi-trace operators on distinct boundaries are considered and studied. As a consequence of these results, the dual theory is expected to factorize in the UV, and the two sectors to be coupled by a soft non-local interaction. A simple field theory model with such behavior is presented.

Figures (21)

• Figure 1: The potential $1/\cos^2 u$. The coordinates are such that we are inside one period and the two AdS boundaries are where the potential blows up. The energies of the associated Schrödinger problem are below zero.
• Figure 2: Left: The $1-1$ correlator with $m=\frac{1}{2}$ as a function of $k$. In the UV it is like the usual $AdS_2$ correlator while in the IR it is gapped with the gap depending on the value of the mass $m$. Right: The same correlator in the case of relevant perturbation ($m^2 = - 0.16$).
• Figure 3: The $1-2$ cross correlator for $m=\frac{1}{2}$ as a function of $k$. The correlator is finite and maximises in the IR $k=0$. It remains similar for relevant perturbations as well (the "bump" becomes sharper).
• Figure 4: Left: The potential for $m^2=-1/16,q^2=1/6,k_r=1/4$. It develops an asymmetric well near the right boundary. The red line is the value of the energy. Right: The potential for $m^2 = -1/6, q^2=1/25, k_r = 1$. It is now asymmetric and unbounded below, the red line again denoting the value of the energy.
• Figure 5: The potential $1/\mathop{\mathrm{cn}}\nolimits^2 u$ for one period of elliptic functions. The coordinates are such that we are inside one period and the two AdS boundaries are where the potential blows up.