Scientific article
Open access

Quantum curves as quantum distributions

Published inJournal of High Energy Physics, vol. 1902, 106
  • Open Access - SCOAP3
Publication date2019

Topological strings on toric Calabi-Yau threefolds can be defined non-perturbatively in terms of a non-interacting Fermi gas of N particles. Using this approach, we propose a definition of quantum mirror curves as quantum distributions on phase space. The quantum distribution is obtained as the Wigner transform of the reduced density matrix of the Fermi gas. We show that the classical mirror geometry emerges in the strongly coupled, large N limit in which ℏ ∼ N . In this limit, the Fermi gas has effectively zero temperature, and the Wigner distribution becomes sharply supported on the interior of the classical mirror curve. The quantum fluctuations around the classical limit turn out to be captured by an improved version of the universal scaling form of Balazs and Zipfel.

  • Matrix Models
  • Topological Strings
Citation (ISO format)
MARINO BEIRAS, Marcos, ZAKANY, Szabolcs. Quantum curves as quantum distributions. In: Journal of High Energy Physics, 2019, vol. 1902, p. 106. doi: 10.1007/JHEP02(2019)106
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Article (Published version)
ISSN of the journal1029-8479

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