Superposition induced topology changes in quantum gravity

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.

87 pages (incl. appendices). v2: updated references

References in corpus (8)

• Black Holes as Effective Geometries
• Anatomy of bubbling solutions
• Linearity of Holographic Entanglement Entropy
• Integrability vs. Information Loss: A Simple Example
• Giant gravitons and the emergence of geometric limits in $\beta$-deformations of $\mathcal{N}=4$ SYM
• Topology and geometry cannot be measured by an operator measurement in quantum gravity
• On Classification Of The Bubbling Geometries
• Reconstructing spacetime from the hologram, even in the classical limit, requires physics beyond the Planck scale

Cited by in corpus (20)

• Operator growth in 2d CFT
• Structure Constants in $\mathcal{N}=4$ SYM at Finite Coupling as Worldsheet $g$-Function
• Submatrix deconfinement and small black holes in AdS
• Interacting systems and wormholes
• Islands with Gravitating Baths: Towards ER = EPR
• Stringy ER=EPR
• Emergent classical spacetime from microstates of an incipient black hole
• BPS coherent states and localization
• Code subspaces for LLM geometries
• Detecting topology change via correlations and entanglement from gauge/gravity correspondence
• Exciting LLM Geometries
• BPS operators in $\mathcal{N}=4$ $SO(N)$ super Yang-Mills theory: plethysms, dominoes and words
• Coherent state operators, giant gravitons, and gauge-gravity correspondence
• Integrable Subsectors from Holography
• Correlations vs connectivity in R-charge
• Quantum Information Processing and Composite Quantum Fields
• Gauged fermionic matrix quantum mechanics
• Interior analysis, stretched technique and bubbling geometries
• Coherent state superpositions, entanglement and gauge/gravity correspondence
• $\mathcal{N}=4$ SYM, (super)-polynomial rings and emergent quantum mechanical symmetries