Dualties of adjoint QCD3 from branes

Abstract

We consider an ‘electric’ U(N) level k QCD3 theory with one adjoint Majorana fermion. Inspired by brane dynamics, we suggest that for k ≥ N/2 the massive m < 0 theory, in the vicinity of the supersymmetric point, admits a mathrm{U}{left(k-frac{N}{2}right)}_{-left(frac{1}{2}k+frac{3}{4}Nright),-left(k+frac{N}{2}right)} ‘magnetic’ dual with one adjoint Majorana fermion. The magnetic theory flows in the IR to a topological mathrm{U}{left(k-frac{N}{2}right)}_{-N,-left(k+frac{N}{2}right)} pure Chern-Simons theory in agreement with the dynamics of the electric theory. When k < N/2 the magnetic dual is mathrm{U}{left(frac{N}{2}-kright)}_{frac{1}{2}k+frac{3}{4}N,N} with one adjoint Majorana fermion. Depending on the sign of the fermion mass, the magnetic theory flows to either mathrm{U}{left(frac{N}{2}-kright)}_{N,N} or mathrm{U}{left(frac{N}{2}-kright)}_{frac{1}{2}N+k,N} TQFT. A second magnetic theory, mathrm{U}{left(N/2+kright)}_{frac{1}{2}k-frac{3}{4}N,N} , flows to either mathrm{U}{left(frac{N}{2}+kright)}_{-N,-N} or mathrm{U}{left(frac{N}{2}+kright)}_{-left(frac{1}{2}N-kright),-N} TQFT. Dualities for SO and USp theories with one adjoint fermion are also discussed.