On non-supersymmetric fixed points in five dimensions

We generalize recent results regarding the phase space of the mass deformed $E_1$ fixed point to a full class of five-dimensional superconformal field theories, known as $X_{1,N}$. As in the $E_1$ case, a phase transition occurs as a supersymmetry preserving and a supersymmetry breaking mass deformations are appropriately tuned. The order of such phase transition could not be unequivocally determined in the $E_1$ case. For $X_{1,N}$ instead, we can show that at large $N$ there exists a regime where the phase transition is second order. Our findings give supporting evidence for the existence of non-supersymmetric fixed points in five dimensions.