Superposition induced topology changes in quantum gravity

Berenstein, David; Miller, Alexandra

doi:10.1007/jhep11(2017)121

Title: Superposition induced topology changes in quantum gravity

Journal Article · Mon Nov 20 00:00:00 EST 2017 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep11(2017)121· OSTI ID:1499190

Berenstein, David ^[1]; Miller, Alexandra ^[1]

Univ. of California, Santa Barbara, CA (United States). Physics Dept.

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.

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Research Organization:: Univ. of California, Santa Barbara, CA (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP)

Grant/Contract Number:: SC0011702

OSTI ID:: 1499190

Journal Information:: Journal of High Energy Physics (Online), Vol. 2017, Issue 11; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 22 works

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