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 \( \mathrm{U}{\left(k-\frac{N}{2}\right)}_{-\left(\frac{1}{2}k+\frac{3}{4}N\right),-\left(k+\frac{N}{2}\right)} \) ‘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 \( \mathrm{U}{\left(\frac{N}{2}-k\right)}_{\frac{1}{2}k+\frac{3}{4}N,N} \) with one adjoint Majorana fermion. Depending on the sign of the fermion mass, the magnetic theory flows to either \( \mathrm{U}{\left(\frac{N}{2}-k\right)}_{N,N} \) or \( \mathrm{U}{\left(\frac{N}{2}-k\right)}_{\frac{1}{2}N+k,N} \) TQFT. A second magnetic theory, \( \mathrm{U}{\left(N/2+k\right)}_{\frac{1}{2}k-\frac{3}{4}N,N} \), flows to either \( \mathrm{U}{\left(\frac{N}{2}+k\right)}_{-N,-N} \) or \( \mathrm{U}{\left(\frac{N}{2}+k\right)}_{-\left(\frac{1}{2}N-k\right),-N} \) TQFT. Dualities for SO and USp theories with one adjoint fermion are also discussed.
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Armoni, A. Dualties of adjoint QCD3 from branes. J. High Energ. Phys. 2022, 73 (2022). https://doi.org/10.1007/JHEP09(2022)073
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DOI: https://doi.org/10.1007/JHEP09(2022)073