Wormholes, Emergent Gauge Fields, and the Weak Gravity Conjecture

TL;DR

This work analyzes the tension between bulk gauge-field reconstruction in AdS/CFT and Hilbert-space factorization when wormholes are present. By decomposing gauge fields into charged constituents, it connects the completeness of charge spectra to the weak gravity conjecture and demonstrates that resolving factorization requires high-energy bulk information, yielding an emergent gauge field in a concrete model. The CP^{N-1} construction provides an explicit framework where emergent electromagnetism arises in the IR, with a Maxwell term generated by integrating out heavy charged fields and a phase structure supporting both Coulomb and confining regimes. The findings offer a cohesive picture in which bulk UV physics underpins low-energy bulk phenomena and has implications for gravitational factorization and interior reconstruction in AdS/CFT.

Abstract

This paper revisits the question of reconstructing bulk gauge fields as boundary operators in AdS/CFT. In the presence of the wormhole dual to the thermofield double state of two CFTs, the existence of bulk gauge fields is in some tension with the microscopic tensor factorization of the Hilbert space. I explain how this tension can be resolved by splitting the gauge field into charged constituents, and I argue that this leads to a new argument for the "principle of completeness", which states that the charge lattice of a gauge theory coupled to gravity must be fully populated. I also claim that it leads to a new motivation for (and a clarification of) the "weak gravity conjecture", which I interpret as a strengthening of this principle. This setup gives a simple example of a situation where describing low-energy bulk physics in CFT language requires knowledge of high-energy bulk physics. This contradicts to some extent the notion of "effective conformal field theory", but in fact is an expected feature of the resolution of the black hole information problem. An analogous factorization issue exists also for the gravitational field, and I comment on several of its implications for reconstructing black hole interiors and the emergence of spacetime more generally.

Figures (8)

• Figure 1: Examples of gauge-invariant operators for electromagnetism on the AdS and AdS-Schwarzschild backgrounds. The directed blue dashed lines represent Wilson lines, and dots with Wilson lines ending (beginning) on them represent local operators creating positive (negative) charge. Wilson lines can also end on the boundary, or be closed into loops. Note that in the AdS-Schwarzschild background there is a new kind of Wilson line, that stretches from one boundary to the other.
• Figure 2: Cutting a Wilson line by a pair of oppositely charged fields. I will argue below that there is a natural "gauge-covariant operator product expansion" that ensures these operators are proportional to each other in low-energy correlation functions. Said differently, the bottom operator flows to the top one under the renormalization group. In the case of a wormhole-threading Wilson line, the lower operator has a simple CFT description since we can represent the left half in the left CFT and the right half in the right CFT.
• Figure 3: Pure electrodyanamics on a spatial cylinder. The integrated electric flux operator $\int_S E\cdot dA$ through any sphere $S$ is nontrivial, but is independent of which sphere we pick.
• Figure 4: Lattice scalar electrodynamics in $1+1$ dimensions. The gauge field is described by assigning an element of $U(1)$ to each link, while the charged scalar is described by adding a complex number to each site. A gauge transformation $V_i$ assigns an element of the group to each site.
• Figure 5: Using the replacement of figure \ref{['cutfig']} to reconstruct a wormhole-threading Wilson line; in the right diagram all operators can be reconstructed using standard techniques.