Numerical study of the $2+1d$ Thirring model with U($2N$)-invariant fermions

In 2+1 dimensions the global U($2N$) symmetry associated with massless Dirac fermions is broken to U($N)\otimes$U($N$) by a parity-invariant mass. I will show how to adapt the domain wall formulation to recover the U($2N$)-invariant limit in interacting fermion models as the domain wall separation is increased. In particular, I will focus on the issue of potential dynamical mass generation in the Thirring model, postulated to take place for $N$ less than some critical $N_c$. I will present results of simulations of the model using both HMC ($N=2$) and RHMC ($N=1$) algorithms, and show that the outcome is very different from previous numerical studies of the model made with staggered fermions, where the corresponding pattern of symmetry breaking is distinct.