Localisation of Dirac modes in gauge theories and Goldstone’s theorem at finite temperature

Matteo Giordano (Department of Theoretical Physics, ELTE Eötvös Loránd University, Pázmány Péter sétány 1/A, Budapest, H-1117, Hungary)

I discuss the possible effects of a finite density of localised near-zero Dirac modes in the chiral limit of gauge theories with N f degenerate fermions. I focus in particular on the fate of the massless quasi-particle excitations predicted by the finite-temperature version of Goldstone’s theorem, for which I provide an alternative and generalised proof based on a Euclidean SU(N f ) A Ward-Takahashi identity. I show that localised near-zero modes can lead to a divergent pseudoscalar-pseudoscalar correlator that modifies this identity in the chiral limit. As a consequence, massless quasi-particle excitations can disappear from the spectrum of the theory in spite of a non-zero chiral condensate. Three different scenarios are possible, depending on the detailed behaviour in the chiral limit of the ratio of the mobility edge and the fermion mass, which I prove to be a renormalisation-group invariant quantity.

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      "value": "I discuss the possible effects of a finite density of localised near-zero Dirac modes in the chiral limit of gauge theories with N  f  degenerate fermions. I focus in particular on the fate of the massless quasi-particle excitations predicted by the finite-temperature version of Goldstone\u2019s theorem, for which I provide an alternative and generalised proof based on a Euclidean SU(N  f  ) A  Ward-Takahashi identity. I show that localised near-zero modes can lead to a divergent pseudoscalar-pseudoscalar correlator that modifies this identity in the chiral limit. As a consequence, massless quasi-particle excitations can disappear from the spectrum of the theory in spite of a non-zero chiral condensate. Three different scenarios are possible, depending on the detailed behaviour in the chiral limit of the ratio of the mobility edge and the fermion mass, which I prove to be a renormalisation-group invariant quantity."
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Published on:
19 December 2022
Publisher:
Springer
Published in:
Journal of High Energy Physics , Volume 2022 (2022)
Issue 12
Pages 1-71
DOI:
https://doi.org/10.1007/JHEP12(2022)103
arXiv:
2206.11109
Copyrights:
The Author(s)
Licence:
CC-BY-4.0

Fulltext files: