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Title: 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 rederive 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. In conclusion, we study other non-linear measurements in the quantum wave-function,more » 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.« less

Authors:
 [1];  [1]
  1. Univ. of California, Santa Barbara, CA (United States). Physics Dept.
Publication Date:
Research Org.:
Univ. of California, Santa Barbara, CA (United States)
Sponsoring Org.:
USDOE Office of Science (SC)
OSTI Identifier:
1499190
Grant/Contract Number:  
SC0011702
Resource Type:
Accepted Manuscript
Journal Name:
Journal of High Energy Physics (Online)
Additional Journal Information:
Journal Name: Journal of High Energy Physics (Online); Journal Volume: 2017; Journal Issue: 11; Journal ID: ISSN 1029-8479
Publisher:
Springer Berlin
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS; AdS-CFT Correspondence; Matrix Models; Models of Quantum Gravity

Citation Formats

Berenstein, David, and Miller, Alexandra. Superposition induced topology changes in quantum gravity. United States: N. p., 2017. Web. doi:10.1007/jhep11(2017)121.
Berenstein, David, & Miller, Alexandra. Superposition induced topology changes in quantum gravity. United States. doi:10.1007/jhep11(2017)121.
Berenstein, David, and Miller, Alexandra. Mon . "Superposition induced topology changes in quantum gravity". United States. doi:10.1007/jhep11(2017)121. https://www.osti.gov/servlets/purl/1499190.
@article{osti_1499190,
title = {Superposition induced topology changes in quantum gravity},
author = {Berenstein, David and Miller, Alexandra},
abstractNote = {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 rederive 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. In conclusion, 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.},
doi = {10.1007/jhep11(2017)121},
journal = {Journal of High Energy Physics (Online)},
number = 11,
volume = 2017,
place = {United States},
year = {2017},
month = {11}
}

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Figures / Tables:

Figure 1 Figure 1: Periodic LLM solutions are characterized by strips. The quantities $n$1, $\tilde{n}$1, $n$2, $\tilde{n}$2 . . . are quantized and can be taken to be integers.

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