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

## TL;DR

This paper investigates the phase transition behavior of an $SU(N) imes U(1)$ gauge theory with many fundamental bosons by analyzing the renormalization group flow and identifying a new stable fixed point indicating a second order phase transition.

## Contribution

It introduces a new stable fixed point in the RG flow for the gauge theory with many bosons, expanding the understanding of phase transitions in such models.

## Key findings

- Discovery of a new stable fixed point for $M > M_{crit}$
- Identification of a second order phase transition
- Calculation of critical exponents in $\e$ and large-$M$ expansions

## Abstract

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.