On the renormalization of the bosonized multi-flavor Schwinger model

Abstract

The phase structure of the bosonized multi-flavor Schwinger model is investigated by means of the differential renormalization group (RG) method. In the limit of small fermion mass the linearized RG flow is sufficient to determine the low-energy behavior of the N-flavor model, if it has been rotated by a suitable rotation in the internal space. For large fermion mass, the exact RG flow has been solved numerically. The low-energy behavior of the multi-flavor model is rather different depending on whether N=1 or N>1, where N is the number of flavors. For N>1 the reflection symmetry always suffers breakdown in both the weak and strong coupling regimes, in contrary to the N=1 case, where it remains unbroken in the strong coupling phase.Comment: 13 pages, 2 figures, final version, published in Physics Letters

Massless fermions in multiflavorQED2

“…We note that the critical value is β 2 c = 8πN/(N − 1) [17], so the spinodal instability always appears at β 2 = 4π. The results of the RG analysis can be easily generalized and can show that the dimensionless couplingũ k tends to constant values in the IR limit.…”

“…As in [6,21] we obtained that the higher modes do not affect the scaling of the fundamental mode. However the other couplings flow by different scaling behavior as obtained by an extended UV RG approach [17,33]. We started the evolution with the WH-RG method then at the scale k SI we turned to the tree level blocking equations.…”

“…The pure QED 2 with N = 1 is not massless since, the tree level blocking gives trivial (which is relevant in d = 2) scaling for the dimensionless couplingũ k so the fermionic mass becomes constant, showing that the cases N = 1 and N = 1 significantly differs [15,17].…”

Renormalization of QCD2

“…The scalar fields are coupled by a mass matrix giving a multi-component or layered sine-Gordon (LSG) model which is used to describe the vortex dynamics of magnetically coupled layered superconductors [24,25], where the number of flavors in QED 2 equals the number of layers of the condensed matter system [14]. The Bose form of the multi-color QCD 2 also contains SG type interactions, a mass matrix and a mixed term.…”

“…One usually takes the bosonized version of these models which are local selfinteracting scalar theories, and can be investigated in an easier way [11,12]. The phase structure of the QED 2 with many flavors was mapped out from its bosonized version and it was shown that it exhibits only a single phase [13,14] as opposed to the single-flavor QED 2 (which is often referred to as the massive Schwinger model) [3-5, 11, 12], which possesses a symmetric strong coupling (e m e ) phase and the weak coupling (e m e ) phase with spontaneously broken reflection symmetry separated by the critical value (m e /e) c ∼ 0.31 as was shown by density matrix renormalization group (RG) technique [15,16] or by continuous RG method [14,17].…”