UV fixed-point structure of the three-dimensional Thirring model

Abstract

We investigate the UV fixed-point structure of the three-dimensional Thirring model by means of the functional renormalization group. We classify all possible 4-fermi interactions compatible with the present chiral and discrete symmetries and calculate the purely fermionic renormalization group flow using a full basis of fermionic four-point functions in the pointlike limit. Our results show that the UV complete (asymptotically safe) Thirring model lies in a two-dimensional coupling plane which reduces to the conventional Thirring coupling only in the strict large-${N}_{\mathrm{f}}$ limit. In addition to the Thirring universality class, which is characterized by one relevant direction (also at finite ${N}_{\mathrm{f}}$), two further interacting fixed points occur which may define new universality classes of second-order phase transitions also involving parity-broken phases. The ${N}_{\mathrm{f}}$ dependence of the Thirring fixed point sheds further light on the existence of an ${N}_{\mathrm{f}}$-controlled quantum phase transition above which chiral symmetry remains unbroken for arbitrary large coupling, even though a definite answer will require a direct computation of competing orders.