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Symmetry theories, Wigner’s function, compactification, and holography

Jonathan J. Heckman1,2,*, Max Hübner3,†, and Chitraang Murdia1,‡

  • *Contact author: jheckman@sas.upenn.edu
  • †Contact author: max-elliot.huebner@physics.uu.se
  • ‡Contact author: murdia@sas.upenn.edu
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Phys. Rev. D 113, 026003 – Published 6 January, 2026

DOI: https://doi.org/10.1103/8jhb-b4pd

Abstract

The global symmetry data of a D-dimensional absolute quantum field theory (QFT) can sometimes be packaged in terms of a (D+1)-dimensional bulk system obtained by extending along an interval, with a relative QFTD at one end and suitable gapped or free boundary conditions at the other end. The partition function of the QFTD can then be interpreted as a wave function depending on background fields. However, in some cases, it is not possible or simply cumbersome to fix an absolute form of the symmetry data. Additionally, it is also of interest to consider entangled and mixed states of relative QFTs as well as entangled and mixed states of gapped or free boundary conditions. We argue that Wigner’s quasiprobabilistic function on phase space provides a physical interpretation of the symmetry data in all such situations. We illustrate these considerations in the case of string compactifications and holographic systems.

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Phys. Rev. D 113, 026003– Published 6 January, 2026
  • Received 22 July 2025
  • Accepted 15 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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