Superposition induced topology changes in quantum gravity

TL;DR

This work shows that spacetime topology in a holographic half‑BPS sector is not an operator—topology can change under superpositions of fixed‑topology states in a limit where the bulk reduces to a free chiral boson. Using a group‑theoretic construction of the chiral boson, the authors build a dual basis from symmetric‑group data (strings) and representations (D‑branes), and derive a Bogoliubov structure that reveals new collective IR modes accompanying topology changes. They demonstrate that topology is encoded in nonlinear wavefunction properties, notably uncertainties and mode entanglement, rather than a single observable, and develop consensus measurements to extract the effective topology from many modes. The paper further develops D‑brane generating operators, MN‑rule encoding via free fermions, and multi‑edge geometries showing how new classical limits with different topology arise from superpositions, with implications for bulk locality, holographic reconstruction, and the role of UV–IR entanglement in emergent geometry.

Abstract

We show that superpositions of classical states in quantum gravity with fixed topology can lead to new classical states with a different topology. We study this phenomenon in a particular limit of the LLM geometries. In this limit, the UV complete minisuperspace of allowed quantum states is exactly given by the Hilbert space of a free chiral boson in two dimensions. We construct this chiral boson purely in terms of combinatorial objects associated with the permutation group. As a byproduct of this analysis, we re-derive the Murnaghan-Nakayama rule for characters of the permutation group. We are able to express this rule in terms of operator relations for raising and lowering operators on the Hilbert space of states in a free fermion basis. Our construction provides a preferred notion of bulk locality by studying an appropriate notion of D-brane state generating functions. We describe how multi-droplet LLM geometries with different topologies give new classical limits of the free chiral boson, even though they can be written as superpositions of coherent states with trivial topology. As a consequence, topology cannot be accessed by a single operator measurement in this quantum system. We study other non-linear measurements in the quantum wave-function, based on uncertainty and entanglement between modes of the chiral boson, that can be used as order parameters to measure the topology of such states.

Figures (9)

• Figure 1: Periodic LLM solutions are characterized by strips. The quantities $n_1, \tilde{n}_1, n_2, \tilde{n}_2\dots$ are quantized and can be taken to be integers.
• Figure 2: Pictorial description of the change of coordinates $(w, \bar{w}) \to (y,\theta)$. The change of variables is area preserving.
• Figure 3: The black and white LLM plane drawing corresponding to a D-brane with fixed energy $n$.
• Figure 4: The black and white LLM plane drawing corresponding to a rectangular Young tableaux with $L\times M$ boxes.
• Figure 5: A schematic depicting possible independent deformations of each edge of an LM state.