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Abstract: Gross-Neveu type models with a finite number of fermion flavours are studiedon a two-dimensional Euclidean space-time lattice. The models areasymptotically free and are invariant under a chiral symmetry. Thesesimilarities to QCD make them perfect benchmark systems for fermion actionsused in large scale lattice QCD computations. The Schroedinger functional forthe Gross-Neveu models is defined for both, Wilson and Ginsparg-Wilsonfermions, and shown to be renormalisable in 1-loop lattice perturbation theory.In two dimensions four fermion interactions of the Gross-Neveu models havedimensionless coupling constants. The symmetry properties of the four fermioninteraction terms and the relations among them are discussed. For Wilsonfermions chiral symmetry is explicitly broken and additional terms must beincluded in the action. Chiral symmetry is restored up to cut-off effects bytuning the bare mass and one of the couplings. The critical mass and thesymmetry restoring coupling are computed to second order in latticeperturbation theory. This result is used in the 1-loop computation of therenormalised couplings and the associated beta-functions. The renormalisedcouplings are defined in terms of suitable boundary-to-boundary correlationfunctions. In the computation the known first order coefficients of thebeta-functions are reproduced. One of the couplings is found to have avanishing beta-function. The calculation is repeated for the recently proposedSchroedinger functional with exact chiral symmetry, i.e. Ginsparg-Wilsonfermions. The renormalisation pattern is found to be the same as in the Wilsoncase. Using the regularisation dependent finite part of the renormalisedcouplings, the ratio of the Lambda-parameters is computed.



Autor: Bjorn Leder

Fuente: https://arxiv.org/







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