Localisation of Dirac modes in gauge theories and Goldstone’s theorem at finite temperature. (English) Zbl 1536.81126
Summary: 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 \(\mathrm{SU}(N_f)_A\) 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.
MSC:
| 81T13 | Yang-Mills and other gauge theories in quantum field theory |
| 81T16 | Nonperturbative methods of renormalization applied to problems in quantum field theory |
| 81T17 | Renormalization group methods applied to problems in quantum field theory |
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