Dualties of adjoint QCD3 from branes

Abstract

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 $$ \mathrm{U}{\left(k-\frac{N}{2}\right)}_{-\left(\frac{1}{2}k+\frac{3}{4}N\right),-\left(k+\frac{N}{2}\right)} $$ U k − N 2 − 1 2 k + 3 4 N , − k + N 2 ‘magnetic’ dual with one adjoint Majorana fermion. The magnetic theory flows in the IR to a topological $$ \mathrm{U}{\left(k-\frac{N}{2}\right)}_{-N,-\left(k+\frac{N}{2}\right)} $$ U k − N 2 − N , − k + N 2 pure Chern-Simons theory in agreement with the dynamics of the electric theory. When k < N/2 the magnetic dual is $$ \mathrm{U}{\left(\frac{N}{2}-k\right)}_{\frac{1}{2}k+\frac{3}{4}N,N} $$ U N 2 − k 1 2 k + 3 4 N , N with one adjoint Majorana fermion. Depending on the sign of the fermion mass, the magnetic theory flows to either $$ \mathrm{U}{\left(\frac{N}{2}-k\right)}_{N,N} $$ U N 2 − k N , N or $$ \mathrm{U}{\left(\frac{N}{2}-k\right)}_{\frac{1}{2}N+k,N} $$ U N 2 − k 1 2 N + k , N TQFT. A second magnetic theory, $$ \mathrm{U}{\left(N/2+k\right)}_{\frac{1}{2}k-\frac{3}{4}N,N} $$ U N / 2 + k 1 2 k − 3 4 N , N , flows to either $$ \mathrm{U}{\left(\frac{N}{2}+k\right)}_{-N,-N} $$ U N 2 + k − N , − N or $$ \mathrm{U}{\left(\frac{N}{2}+k\right)}_{-\left(\frac{1}{2}N-k\right),-N} $$ U N 2 + k − 1 2 N − k , − N TQFT. Dualities for SO and USp theories with one adjoint fermion are also discussed.