Dualties of adjoint QCD3 from branes

We consider an 'electric' U(N) level k QCD(3) 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)(-(1/2k+3/4N),-(k+N/2)) '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)) 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)(1/2k+3/4N,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) or U(N/2 - k)(1/2N+k,N) TQFT. A second magnetic theory, U(N/2 + k)1/2k-3/4N,-N, flows to either U(N/2 + k)(-N,-N) or U(N/2 + k)(-(1/2N-k),-N) TQFT. Dualities for SO and USp theories with one adjoint fermion are also discussed.

Automated summary

This article considers an 'electric' U(N) level k QCD(3) theory with one adjoint Majorana fermion and explores its dual theories near the supersymmetric point. Two magnetic dual theories are obtained based on different parameter ranges, and duality for SO and USp theories is also discussed.