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Towards critical physics in 2+1d with U(2N )-invariant fermions / Simon, Hands
Journal of High Energy Physics, Volume: 2016, Issue: 11
Swansea University Author: Simon, Hands
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Interacting theories of N relativistic fermion flavors in reducible spinor rep- resentations in 2+1 spacetime dimensions are formulated on a lattice using domain wall fermions (DWF), for which a U(2N) global symmetry is recovered in the limit that the wall separation Ls is made large. The Gross-Neve...
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Interacting theories of N relativistic fermion flavors in reducible spinor rep- resentations in 2+1 spacetime dimensions are formulated on a lattice using domain wall fermions (DWF), for which a U(2N) global symmetry is recovered in the limit that the wall separation Ls is made large. The Gross-Neveu (GN) model is studied in the large-N limit and an exponential acceleration of convergence to the large-Ls limit is demonstrated if the usual parity-invariant mass mψ ̄ψ is replaced by the U(2N)-equivalent im3ψ ̄γ3ψ. The GN model and two lattice variants of the Thirring model are simulated for N = 2 using a hybrid Monte Carlo algorithm, and studies made of the symmetry-breaking bilinear con- densate and its associated susceptibility, the axial Ward identity, and the mass spectrum of both fermion and meson excitations. Comparisons are made with existing results ob- tained using staggered fermions. For the GN model a symmetry-breaking phase transition is observed, the Ward identity is recovered, and the spectrum found to be consistent with large-N expectations. There appears to be no obstruction to the study of critical UV fixed-point physics using DWF. For the Thirring model the Ward identity is not recovered, the spectroscopy measurements are inconclusive, and no symmetry breaking is observed all the way up to the effective strong coupling limit. This is consistent with a critical Thirring flavor number Nc < 2, contradicting earlier staggered fermion results.
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