Dualities of Adjoint QCD${}_3$ from Branes

Abstract

We consider an 'electric' $U(N)$ level $k$ QCD${}_3$ theory with one adjoint Majorana fermion. Inspired by brane dynamics, we suggest that for $k\ge N/2$ the massive $m<0$ theory, in the vicinity of the supersymmetric point, admits a $U(k-\frac{N}{2}{)}_{-(\frac{1}{2}k+\frac{3}{4}N),-(k+\frac{N}{2})}$ 'magnetic' dual with one adjoint Majorana fermion. The magnetic theory flows in the IR to a topological $U(k-\frac{N}{2}{)}_{-N,-(k+\frac{N}{2})}$ pure Chern-Simons theory in agreement with the dynamics of the electric theory. When $k<N/2$ the magnetic dual is $U(\frac{N}{2}-k{)}_{\frac{1}{2}k+\frac{3}{4}N,N}$ with one adjoint Majorana fermion. Depending on the sign of the fermion mass, the magnetic theory flows to either $U(\frac{N}{2}-k{)}_{N,N}$ or $U(\frac{N}{2}-k{)}_{\frac{1}{2}N+k,N}$ TQFT. A second magnetic theory, $U(N/2+k{)}_{\frac{1}{2}k-\frac{3}{4}N,-N}$, flows to either $U(\frac{N}{2}+k{)}_{-N,-N}$ or $U(\frac{N}{2}+k{)}_{-(\frac{1}{2}N-k),-N}$ TQFT. Dualities for $SO$ and $USp$ theories with one adjoint fermion are also discussed.

12 pages, 3 figures. v2: figure 2 corrected. v3: fixed the U(1) level throughout the paper. Accepted to JHEP. v4: a typo in the title(!) fixed. Thanks, Prem, for spotting it

References in corpus (3)

• Level/rank Duality and Chern-Simons-Matter Theories
• Seiberg Duality in Chern-Simons Theory
• Level-Rank Duality in Chern-Simons Theory from a Non-Supersymmetric Brane Configuration

Cited by in corpus (3)

• Anomalies and Symmetry Fractionalization
• 5d SCFTs and their non-supersymmetric cousins
• Dualities of 3D $\mathcal{N}=1$ SQCD from Branes and non-SUSY deformations