Fermionic theories and dualities in 2+1 dimensions

Title: Fermionic theories and dualities in 2+1 dimensions

Abstract: Dirac fermions and their self-interactions play a key role in particle physics and condensed matter, and exhibit interesting phenomena such as universality at conformal critical points, chiral symmetry breaking, and the dynamical generation of fermion mass. In this talk, I discuss critical Gross-Neveu theories in 2+1 dimensions using the renormalisation group. After introducing the method of functional renormalisation and its application to U(N) fermionic theories, I will demonstrate how classically irrelevant six-fermion interactions become exactly marginal at large N, leading to a line of UV fixed points. At the endpoints of this line, mass is generated spontaneously following the breaking of scale symmetry, in a manner reminiscent of the Bardeen-Moshe-Bander phenomenon in scalar O(N) theories. I will further discuss aspects of chiral symmetry breaking and the dynamical generation of fermion mass, and an exact duality map between Gross-Neveu and Gross-Neveu-Yukawa theories.