Towards Critical Physics in 2+1d with U(2N)-Invariant Fermions

Understand

Interacting theories of N relativistic fermion flavors in reducible spinor representations 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 $L_s$ is made large.

• The Gross-Neveu (GN) model is studied in the large-N limit and an exponential acceleration of convergence to the large-$L_s$ limit is demonstrated if the usual parity-invariant mass $m\bar\psi\psi$ is replaced by the U(2N)-equivalent $im_3\bar\psi\gamma_3\psi$.
• 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 condensate and its associated susceptibility, the axial Ward identity, and the mass spectrum of both fermion and meson excitations.
• Comparisons are made with existing results obtained using staggered fermions.