Disorder Averaging and its UV (Dis)Contents

TL;DR

The paper develops a string-theory framework to realize disorder averaging over QFT couplings in up to four spacetime dimensions by engineering multiple brane-localized sectors with varying moduli. It shows that if each sector is holographic, the bulk can be interpreted as a single AdS throat corresponding to an ensemble-averaged boundary theory, while enabling a UV-complete counterexample to claims that holography can be developed without UV completion. The authors connect their construction to MM's baby universe picture and McNamara–Vafa Swampland constraints, arguing that the UV completion becomes invalid only at high energies or for highly entangled states, thus providing an explicit counterexample to claims that EFT/Holography can always decouple from UV. They provide extensive D=4,3,2,1 examples using D3/D7 stacks, brane boxes, and Calabi–Yau fibrations to realize different distributions, and discuss limitations and directions, including potential implications for the Page curve and future UV completions.

Abstract

We present a stringy realization of quantum field theory ensembles in $D \le 4$ spacetime dimensions, thus realizing a disorder averaging over coupling constants. When each member of the ensemble is a conformal field theory with a standard semi-classical holographic dual of the same radius, the resulting bulk can be interpreted as a single asymptotically Anti-de Sitter space geometry with a distribution of boundary components joined by wormhole configurations, as dictated by the Hartle-Hawking wave function. This provides a UV completion of a recent proposal by Marolf and Maxfield that there is a high-dimensional Hilbert space for baby universes, but one that is compatible with the proposed Swampland constraints of McNamara and Vafa. This is possible because our construction is really an approximation that breaks down both at short distances, but also at low energies for objects with a large number of microstates. The construction thus provides an explicit set of counterexamples to various claims in the literature that holographic and effective field theory considerations can be reliably developed without reference to any UV completion.

Figures (6)

• Figure 1: Copies of the same QFT sector separated from one another in the extra dimensions. QFTs are engineered on the worldvolume of branes (colored grey). The extra-dimensional geometry is colored blue.
• Figure 2: On the left, the string theory construction builds a large number of $D$-dimensional CFTs, each of which has its own dual AdS throat. The closed subset of operators defined by the $\mathbb{O}$s, however, only reconstructs a single AdS throat, which is dual to an ensemble-averaged CFT, shown on the right.
• Figure 3: The presence of Euclidean wormholes results in non-factorization of the gravitational path integral.
• Figure 4: Quiver diagram of the 4D $\mathcal{N} = 2$ SCFT obtained from $N_\text{c}$ D3-branes probing $\mathbb{C}^2 / \mathbb{Z}_M$, for $M = 4$. Each node represents an $\mathop{\mathrm{SU}}\nolimits(N_\text{c})$ gauge group, and links between them denote bifundamental hypermultiplets.
• Figure 5: D4/NS5 system leading to the 4D quiver gauge theory. Each D4-brane segment corresponds to a gauge group, whose coupling is set by the relative distance in the 6 direction between the two boundary NS5-branes as $\frac{1}{g_i^2}=\frac{x_{i + 1}^6 - x_i^6}{g_\text{s} \sqrt{\alpha'}}$. The effective 4D SCFT on the D4-brane worldvolume is the same quiver gauge theory shown in \ref{['fig:N=2 quiver']}.