nLab D=3 N=2 super Yang-Mills theory

Idea

The special case of super Yang-Mills theory in dimension 3 and number of supersymmetries 2.

Properties

• 3d-3d correspondence

Related concepts

On ordinary Yang-Mills theory (YM):

• D=2 YM, D=3 YM, D=4 YM, D=5 YM, D=6 YM, D=7 YM, D=8 YM

• Maxwell theory/electromagnetism (U(1) YM), Donaldson theory (SU(2) YM), quantum chromodynamics (SU(3) YM)

• Yang-Mills equation, linearized Yang-Mills equation, Yang-Mills instanton, Yang-Mills field, stable Yang-Mills connection, Yang-Mills moduli space, Yang-Mills flow, F-Yang-Mills equation, Bi-Yang-Mills equation

• Uhlenbeck's singularity theorem, Uhlenbeck's compactness theorem

On variants of Yang-Mills theory and on super Yang-Mills theory (SYM):

• Yang-Mills-Higgs equations, stable Yang-Mills-Higgs pair, Yang-Mills-Higgs flow

• Einstein-Yang-Mills theory, Einstein-Yang-Mills-Dirac theory, Einstein-Yang-Mills-Dirac-Higgs theory

• 3D Yang-Mills-Chern-Simons theory

• 3d superconformal gauge field theory: D=3 N=1 SYM, D=3 N=2 SYM, D=3 N=4 SYM

• 4d superconformal gauge field theory: D=4 N=1 SYM, D=4 N=2 SYM, D=4 N=4 SYM

• D=5 SYM, D=6 SYM, D=7 SYM, D=10 SYM

• topological Yang-Mills theory, topologically twisted D=4 super Yang-Mills theory

References

• Jan de Boer, Kentaro Hori, Yaron Oz, Dynamics of N=2 Supersymmetric Gauge Theories in Three Dimensions, Nucl. Phys. B500:163-191, 1997 (arXiv:hep-th/9703100)

• Ofer Aharony, Amihay Hanany, Kenneth Intriligator, Nathan Seiberg, Matthew Strassler,

  Aspects of $\mathcal{N}=2$ Supersymmetric Gauge Theories in Three Dimensions, Nucl. Phys. B499:67-99, 1997 (arXiv:hep-th/9703110)

On the Witten index for D=3 N=2 super Yang-Mills theory:

• Mathew Bullimore, Andrea E. V. Ferrari, Heeyeon Kim, The 3d Twisted Index and Wall-Crossing (arXiv:1912.09591)

Relation to quantum K-theory rings:

Relation to D=3 N=2 super Yang-Mills theory:

• Hans Jockers, Peter Mayr, A 3d Gauge Theory/Quantum K-Theory Correspondence, Advances in Theoretical and Mathematical Physics 24 2 (2020) [arXiv:1808.02040, doi:10.4310/ATMP.2020.v24.n2.a4]

Construction in M-theory:

• Marwan Najjar, Jiahua Tian, Yi-Nan Wang, 3d $\mathcal{N}=2$ theories from M-theory on CY4 and IIB brane box [arXiv:2312.17082]

• Andrea Sangiovanni, Roberto Valandro: M-theory geometric engineering for rank-0 3d $\mathcal{N}=2$ theories [arXiv:2410.13943]