"Filtering" CFTs at large N: Euclidean Wormholes, Closed Universes, and Black Hole Interiors

In the quest to understand the universe, physicists have long relied on a powerful idea called holography. This concept suggests that a three-dimensional world containing gravity, like the space inside a black hole, can be completely described by a two-dimensional surface surrounding it, much like a hologram encodes a 3D image on a flat sheet. This surface is a quantum field theory, a mathematical framework describing how particles and forces behave without gravity. For decades, scientists have used this connection to translate difficult problems in gravity into easier problems in quantum physics, and vice versa. However, a persistent puzzle has remained: when physicists calculate the behavior of these quantum systems at very large scales, the results sometimes refuse to match the smooth, predictable geometry of the universe we expect to see. Specifically, the quantum calculations sometimes produce erratic, jagged fluctuations that seem to have no place in the smooth fabric of spacetime, and they sometimes fail to separate cleanly into independent parts, a property that the gravitational side of the equation demands.

A new paper by Hong Liu at the Massachusetts Institute of Technology proposes a solution to this mismatch by introducing a new kind of filter. The author suggests that the connection between the quantum surface and the gravitational interior is not a direct, one-to-one copy of every tiny detail. Instead, the process of mapping the quantum world to the gravitational world involves a projection that smooths out the erratic, jagged fluctuations inherent in the quantum calculations. By filtering out these irregularities, the remaining smooth part of the quantum data perfectly matches the smooth geometry of gravity. This simple act of filtering does more than just fix a mathematical error; it reveals that the strange, disconnected pieces of the quantum world are actually the source of some of the most exotic features of gravity, including wormholes and the hidden interiors of black holes.

The core of the problem lies in how the two sides of the holographic dictionary handle large numbers. On the quantum side, the theory depends on a parameter that represents the number of degrees of freedom, often thought of as the number of particles or fields. As this number grows very large, the theory is expected to settle into a predictable pattern. However, the author argues that the quantum partition function—a calculation that sums up all possible states of the system—contains two distinct parts. One part is smooth and follows a predictable pattern as the number of degrees of freedom increases. The other part is erratic, behaving in a jagged, unpredictable way that does not fit into any standard mathematical series. In the past, physicists assumed these erratic parts would average themselves out and disappear, leaving only the smooth behavior. But the paper argues that these erratic parts do not vanish; instead, they are the key to understanding why gravity behaves the way it does.

When the author applies a "filter" to the quantum calculation, removing the erratic part and keeping only the smooth part, the result matches the gravitational path integral perfectly. This filter acts as a definition for what we mean by the gravitational average. Without this filter, the quantum calculation would not factorize, meaning it would not break down into independent pieces when the system is split into separate parts. This failure to factorize is a major puzzle because it implies that the quantum theory is not a single, unified system but rather an average over many different possibilities. The new proposal resolves this by showing that the factorization failure is an illusion caused by the erratic parts. When those parts are filtered out, the smooth remainder behaves exactly as a single, unified quantum system should, while the filtered-out erratic parts are responsible for the wormhole connections that link different regions of space.

One of the most striking findings is that these wormholes, which are tunnels connecting different regions of spacetime, are not random accidents but are direct reflections of the correlations in the erratic quantum data. The paper shows that the strength of a wormhole connecting two separate regions is determined by how the erratic parts of the quantum calculations for those two regions correlate with each other. This provides a concrete way to calculate the probability of a wormhole appearing without needing to assume the existence of a random ensemble of universes. Instead, the wormhole is a natural consequence of the specific, messy details of the quantum theory that are usually hidden from view.

This framework also changes our understanding of the interior of black holes and the existence of closed universes. The author argues that the smooth geometry we imagine inside a black hole is actually an emergent feature that only appears after the erratic quantum fluctuations are filtered out. If an observer were to look closely at the quantum data without this filter, they would see a chaotic, volatile structure. The paper suggests that the interior of a black hole is "quantum volatile," meaning that its geometry fluctuates wildly at a fundamental level, even if those fluctuations are smoothed over when we look at the large-scale picture. This volatility is not a breakdown of physics but a fundamental property of the quantum description.

The same logic applies to closed universes, which are self-contained pockets of spacetime with no boundary, often called baby universes. The paper demonstrates that these baby universes emerge from the erratic correlations of the quantum theory. When a quantum system is entangled with a baby universe, the connection is mediated by these erratic fluctuations. The author shows that the existence of the baby universe and its entanglement with our own universe are direct consequences of the fact that the quantum theory contains these jagged, non-smooth parts. Without them, the baby universe would not exist.

Furthermore, the paper addresses the issue of global symmetries, which are rules that govern how particles interact. In quantum gravity, it is widely believed that exact global symmetries cannot exist because they can be broken by wormholes. The new perspective explains this by showing that the symmetry appears to hold in the smooth, filtered version of the theory, but the wormhole connections, which arise from the erratic parts, break it. This provides a clear mechanism for how a symmetry can be present in the low-energy world but absent in the fundamental theory.

The author also derives a set of mathematical inequalities that constrain the possible amplitudes of these wormholes. These inequalities act as a consistency check, ensuring that the correlations between the erratic parts of the quantum theory do not lead to impossible physical scenarios. This infinite tower of constraints offers a new way to test the validity of the holographic principle and the nature of wormholes.

In the context of black holes, the paper suggests that the interior is fundamentally different from the exterior. While the outside of a black hole looks smooth and predictable, the inside is subject to these large, erratic fluctuations. An observer falling into a black hole might not notice this volatility because they do not have enough time to measure the fluctuations before reaching the singularity. However, the theory implies that the geometry they are traversing is not a fixed, solid structure but a volatile, fluctuating entity. This challenges the traditional view of the black hole interior as a stable, classical region of spacetime.

The paper concludes by suggesting that this "filtered" view of the holographic dictionary offers a more complete picture of how spacetime emerges from quantum mechanics. It resolves the factorization puzzle, explains the origin of wormholes, and provides a mechanism for the emergence of closed universes and black hole interiors. By recognizing that the smooth geometry of gravity is a filtered version of a more complex, erratic quantum reality, the author provides a unified framework that connects the messy details of the quantum world to the elegant structure of the cosmos. This approach does not require the existence of a random ensemble of theories but instead relies on the intrinsic properties of a single quantum system, offering a clearer path toward understanding the deep connection between quantum mechanics and gravity.