Phase Transition of SU(N)×U(1) Theory with m Fundamental Bosons

The phase transition in the case of Ginzburg-Landau theory is well studied in both the ε-exapansion and also in the large boson number expansion. The natural question that comes next is what happens if there is also a non-abelian SU(N) gauge field is present. This question is also important as it has been found that in SU(m) anti-ferromagnets on a square lattice with spins that sit at A and B sub lattices are in the representation described by the Young tableau with N rows in one sub-lattice and m − N in other. Then under the Schwinger boson representation and in the Large-m limit the theory can be described as a SU(N)×U(1) theory with m species of fundamental bosons. The phases for N=1 are known. Here, we study the problem for general N, calculate the beta function, and find a stable fixed point in the zero mass plane for m>m_crit, indicating a second order phase transition. The critical exponents are calculated in the 4-d expansion and in the large-m expansion.