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Confinement in non-Abelian lattice gauge theory via persistent homology

Daniel Spitz1,*, Julian M. Urban2,3, and Jan M. Pawlowski1,4

  • 1Institut für Theoretische Physik, Universität Heidelberg, Philosophenweg 16, D-69120 Heidelberg, Germany
  • 2Center for Theoretical Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA
  • 3The NSF AI Institute for Artificial Intelligence and Fundamental Interactions, Cambridge, Massachusetts 02139, USA
  • 4ExtreMe Matter Institute EMMI, GSI, Planckstraße 1, D-64291 Darmstadt, Germany

  • *spitz@thphys.uni-heidelberg.de
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Phys. Rev. D 107, 034506 – Published 16 February, 2023

DOI: https://doi.org/10.1103/PhysRevD.107.034506

Abstract

We investigate the structure of confining and deconfining phases in SU(2) lattice gauge theory via persistent homology, which gives us access to the topology of a hierarchy of combinatorial objects constructed from given data. Specifically, we use filtrations by traced Polyakov loops, topological densities, holonomy Lie algebra fields, as well as electric and magnetic fields. This allows for a comprehensive picture of confinement. In particular, topological densities form spatial lumps which show signatures of the classical probability distribution of instanton-dyons. Signatures of well-separated dyons located at random positions are encoded in holonomy Lie algebra fields, following the semiclassical temperature dependence of the instanton appearance probability. Debye screening discriminating between electric and magnetic fields is visible in persistent homology and pronounced at large gauge coupling. All employed constructions are gauge-invariant without a priori assumptions on the configurations under study. This work showcases the versatility of persistent homology for statistical and quantum physics studies, barely explored to date.

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Phys. Rev. D 107, 034506– Published 16 February, 2023
  • Received 1 December 2022
  • Accepted 27 January 2023
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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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