Phase transition in SU(N)×U(1) gauge theory with many fundamental bosons

Here we study the renormalization group flow of $SU(N)\ifmmode\times\else\texttimes\fi{}U(1)$ gauge theory with $M$-fundamental bosons in $4\ensuremath{-}\ensuremath{\epsilon}$ dimension by calculating the beta functions. We found a new stable fixed point in the zero mass plane for $M>{M}_{\mathrm{crit}}$ by expanding up to $O(\ensuremath{\epsilon})$. This indicates a second-order phase transition. We also calculated the critical exponents in both $\ensuremath{\epsilon}$ expansion and also in the large-$M$ expansion.