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Localization in the Dirac spectrum and gauge-field topology

Claudio Bonanno1,* and Matteo Giordano2,†

  • *Contact author: claudio.bonanno@csic.es
  • †Contact author: giordano@bodri.elte.hu
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Phys. Rev. D 111, 114515 – Published 20 June, 2025

DOI: https://doi.org/10.1103/yzbb-7yp9

Abstract

We study localization of the low Dirac modes in 3+1 dimensional pure SU(3) gauge theory at zero and nonzero imaginary θ angle, with the aim of better characterizing the relation between low-mode localization and topological features of gauge theories. We show that the mobility edge observed in the deconfined phase at θ=0 is present also at nonzero θ, appearing exactly at the deconfinement transition. We find that the mobility edge is affected by topology only indirectly, through its effects on the ordering of the Polyakov loop. Moreover, the change in the mobility edge is strongly correlated with the change in the Polyakov-loop expectation value, both as one moves along the critical line, and as one departs from it toward higher temperatures. This further strengthens the connection between low-mode localization and deconfinement, showing in particular the key role played by the ordering of the Polyakov loop.

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Phys. Rev. D 111, 114515– Published 20 June, 2025
  • Received 2 April 2025
  • Accepted 27 May 2025
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