An asymptotic-safety mechanism for chiral Yukawa systems

We introduce Weinberg's idea of asymptotic safety and pave the way towards an asymptotically safe chiral Yukawa system with a $U(N_L)_L \otimes U(1)_R$ symmetry in a leading-order derivative expansion using nonperturbative functional RG equations. As a toy model sharing important features with the standard model we explicitely discuss N_L=10 for which we find a non-Gaussian fixed point and compute its critical exponents. We observe a reduced hierarchy problem as well as predictions for the toy Higgs and the toy top mass.