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θ-vacuum from functional renormalization

Yuepeng Guan1, Jan M. Pawlowski2,3, and Masatoshi Yamada4

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Phys. Rev. D 113, 025003 – Published 6 January, 2026

DOI: https://doi.org/10.1103/pryh-22dx

Abstract

We study topological properties of a quantum mechanical system with U(1) symmetry within the functional renormalization group approach. These properties include the vacuum energy structure and the topological susceptibility. Our approach works with a complexification of the flow equation, and specifically, we embed the original symmetry into the complex plane, U(1)→C. We compute the effective potential of a given topological sector by restricting ourselves to field configurations with given generalized nontrivial Chern-Simons numbers. The full potential is directly constructed from these sector potentials. Our results compare well with the benchmark results obtained from solving the corresponding Schrödinger equation.

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Phys. Rev. D 113, 025003– Published 6 January, 2026
  • Received 9 August 2025
  • Accepted 18 December 2025
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Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI. Funded by SCOAP3.

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