Temperature dependence of the anomalous effective action of fermions in two and four dimensions

Abstract

The temperature dependence of the anomalous sector of the effective action of fermions coupled to external gauge and pseudo-scalar fields is computed at leading order in an expansion in the number of Lorentz indices in two and four dimensions. The calculation preserves chiral symmetry and confirms that a temperature dependence is compatible with axial anomaly saturation. The result checks soft-pions theorems at zero temperature as well as recent results in the literature for the pionic decay amplitude into static photons in the chirally symmetric phase. The case of chiral fermions is also considered.

Anomalous processes at high temperature and density in a two-dimensional linear σ model

“…defined above, and has one power of the mass m less when compared to the π o γ amplitude, in agreement with the general arguments of [1,2,12].…”

“…The reason why the non-locality of this coupling has been missed in [12] can be traced back in a misuse of the imaginary time techniques to get the zero momenta limit.…”

“…Salcedo in [12] gives also general arguments according to which π o → 2γ (or π o → γ in two dimensions) should vanish in the chiral phase, and be replaced by amplitudes involving the σ meson. From a technical perspective, the common point of all these studies is the use at some stage of the imaginary time formalism, in the limit of vanishing external momenta.…”

Anomalies for nonlocal dirac operators

“…The Wigner transformation method combined with the ζ-function regularization has been further extended to the finite temperature case in [28,29]. As is well known, in the imaginary time formulation of finite temperature field theory, the field configurations are periodic or antiperiodic functions of the Euclidean time for bosons and fermions respectively and thus the frequency running in the fermion loop takes discrete values only, ω n = π(2n+1)T (where T stands for the temperature and n is any integer) which are known as Matsubara frequencies.…”

“…In Ref. [28] this method has been applied to compute the anomalous component of the effective action of two-and four-dimensional fermions at finite temperature in the presence of arbitrary vector and axial gauge fields and scalar and pseudoscalar fields on the chiral circle. The computation is carried out to leading order in a suitable commutator which preserves chiral symmetry.…”