Superposition induced topology changes in quantum gravity

TL;DR

This paper demonstrates how superpositions of classical quantum gravity states can induce topology changes, using a model based on free chiral bosons and permutation group combinatorics, revealing new classical limits and measurement challenges.

Contribution

It introduces a novel approach to understanding topology changes in quantum gravity through superpositions and combinatorial models, connecting to LLM geometries and operator-based topology measurements.

Findings

Superpositions can produce states with different topologies.

A combinatorial construction of the chiral boson reproduces key group character rules.

Topology cannot be distinguished by single operator measurements in this quantum system.

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.