Phase Transition In SU(N)times U(1) Gauge Theory With Many Fundamental Bosons

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