On the equivalence of renormalizations in standard and dimensional regularizations of 2D four-fermion interactions

Three-loop renormalization of the SU(N) non-abelian Thirring model

“…Therefore due to the presence of the factors of (d − 2) in (5.5) counterterms are only required for O 11 , O 30 and O 31 which have an odd number of γ-matrices. This is consistent with the earlier observation relating to chirality, [21,22]. The generation of the latter operators affects the two loop renormalization.…”

“…This absence of multiplicative renormalizability in Thirring like models has already been recognized in the work of [15,20,21,22] upon which a lot of our calculation is founded. Though in [15] the NATM was only discussed at the level of the two loop β-function and anomalous dimension, whilst [21,22] extended the wave function renormalization to three loops. These papers were important for our determination of the β-function, anomalous dimension and mass anomalous dimension at three loops, which is our central aim.…”

“…These are the evanescent operators we referred to earlier. In the context of the ABTM their presence has been noted before in [15,21,22] and the most general (abelian) scenario discussed in [15,20]. In both instances the analysis has been to two loops, though in [22] the consequences for the three loop wave function renormalization were also discussed.…”

“…Otherwise the contractions are across the tensor product. In general, rules for the treatment of the Γ (n) -basis have been developed, [27], and then applied to the three loop 2-point function, [21,22]. We have not used the majority of these as they prove too cumbersome to implement symbolically.…”

“…Due to these technical reasons, which will be explicitly detailed later, we concentrate on presenting a comprehensive discussion on the full renormalization of the NATM. Moreover, due to the nature of the renormalization we have also found it necessary to comprehensively study a variety of mass independent renormalization schemes, aside from the widely used MS scheme, to ensure consistency from other considerations, [15,21,22]. This is guided very much by the fact that in two dimensions Thirring models are equivalent by, for instance Fierz rearrangements, to other four-fermi models such as the Gross Neveu model for certain values of N f and N c .…”