Phys. Rev. D 109, 105019 (2024) - Quantum duality in electromagnetism and the fine structure constant
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Quantum duality in electromagnetism and the fine structure constant

Clay Córdova and Kantaro Ohmori
Phys. Rev. D 109, 105019 – Published 13 May 2024
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  • INTRODUCTION
  • ELECTRIC-MAGNETIC DUALITY
  • DUALITIES, GAUGING, AND SYMMETRIES
  • NONINVERTIBLE SYMMETRY ACTION
  • ACKNOWLEDGMENTS
    • References

    Abstract

    We describe the interplay between electric-magnetic duality and higher symmetry in Maxwell theory. When the fine structure constant is rational, the theory admits noninvertible symmetries which can be realized as composites of electric-magnetic duality and gauging a discrete subgroup of the one-form global symmetry. These noninvertible symmetries are approximate quantum invariances of the natural world which emerge in the infrared below the mass scale of charged particles. We construct these symmetries explicitly as topological defects and illustrate their action on local and extended operators. We also describe their action on boundary conditions and illustrate some consequences of the symmetry for Hilbert spaces of the theory defined in finite volume.

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    • Received 30 March 2024
    • Accepted 25 April 2024

    DOI:https://doi.org/10.1103/PhysRevD.109.105019

    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.

    Published by the American Physical Society

    Physics Subject Headings (PhySH)

    1. Research Areas
    Dualities in field theoryGauge theoriesNonperturbative effects in field theoryQuantum electrodynamicsQuantum field theorySymmetriesTopological field theories
    1. Techniques
    DualityTopology
    Particles & Fields

    Authors & Affiliations

    Clay Córdova1 and Kantaro Ohmori2

    • 1Enrico Fermi Institute and Kadanoff Center for Theoretical Physics, University of Chicago, Chicago, Illinois 60637, USA
    • 2Faculty of Science, University of Tokyo, Tokyo 113-0033, Japan

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    Issue

    Vol. 109, Iss. 10 — 15 May 2024

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    • Figure 1
      Figure 1

      The S action on a boundary condition B. The symmetry defect (red) collides with B to make a new boundary condition B·S, with AL a new boundary field.

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    • Figure 2
      Figure 2

      Illustration of (66). The closed cycle γL−γR links with the Poincaré dual of y in W, and the total holonomy (66) takes a fractional value. This implies the presence of an electric one-form symmetry defect (a surface operator) on the Poincaré dual of y (red).

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    • Figure 3
      Figure 3

      The topological move that proves (90). Both the toroidal cavity and a cross section are illustrated. (a) The configuration defining HC,B. The red ring is the condensate C, and the toroidal cavity has the boundary condition B. (b) The condensate C is replaced by the toroidal duality defect D=DNe,Nm using the fusion rules for D×D¯. (c) The duality defect is topological and can be pushed onto the boundary, changing the boundary condition to B·D.

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