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