Exact-WKB, complete resurgent structure, and mixed anomaly in quantum mechanics on S1

Sueishi, Naohisa; Kamata, Syo; Misumi, Tatsuhiro; Ünsal, Mithat

doi:10.1007/jhep07(2021)096

Exact-WKB, complete resurgent structure, and mixed anomaly in quantum mechanics on S¹

Journal Article · Thu Jul 15 00:00:00 EDT 2021 · Journal of High Energy Physics (Online)

DOI:https://doi.org/10.1007/jhep07(2021)096· OSTI ID:1849459

Sueishi, Naohisa ^[1]; Kamata, Syo ^[2]; Misumi, Tatsuhiro ^[3]; Ünsal, Mithat ^[4]

Nagoya Inst. of Technology (Japan). Dept. of Physics; North Carolina State Univ., Raleigh, NC (United States)
National Centre for Nuclear Research, Warsaw (Poland)
Akita Univ., Akita (Japan). Dept. of Mathematical Science; Keio Univ., Kanagawa (Japan). Dept. of Physics
North Carolina State Univ., Raleigh, NC (United States). Dept. of Physics

We investigate the exact-WKB analysis for quantum mechanics in a periodic potential, with N minima on S¹. We describe the Stokes graphs of a general potential problem as a network of Airy-type or degenerate Weber-type building blocks, and provide a dictionary between the two. The two formulations are equivalent, but with their own pros and cons. Exact-WKB produces the quantization condition consistent with the known conjectures and mixed anomaly. The quantization condition for the case of N-minima on the circle factorizes over the Hilbert sub-spaces labeled by discrete theta angle (or Bloch momenta), and is consistent with ’t Hooft anomaly for even N and global inconsistency for odd N. By using Delabaere-Dillinger-Pham formula, we prove that the resurgent structure is closed in these Hilbert subspaces, built on discrete theta vacua, and by a transformation, this implies that fixed topological sectors (columns of resurgence triangle) are also closed under resurgence.

View Accepted Manuscript (DOE)

Research Organization:: North Carolina State University, Raleigh, NC (United States)

Sponsoring Organization:: USDOE Office of Science (SC)

Grant/Contract Number:: FG02-03ER41260

OSTI ID:: 1849459

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 7 Vol. 2021; ISSN 1029-8479

Publisher:: Springer NatureCopyright Statement

Country of Publication:: United States

Language:: English

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