nLab D=3 Yang-Mills theory

Idea

Yang-Mills theory in spacetime dimension $D = 1+2$.

Related entries

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

• D=3 Yang-Mills-Chern-Simons theory

• Maxwell-Chern-Simons theory

References

Suggestion to consider the Yang-Mills mass gap problem for 3D YM theory:

• Edward Witten; p 8 of: Physical Law and the Quest for Mathematical Understanding, Bulletin of the AMS 40 1 (2002) 21-29 [doi:10.1090/S0273-0979-02-00969-2, pdf, pdf]

Claim of derivation of the Yang-Mills mass gap in 3D (though non-constructive):

• Dimitra Karabali, V. Parameswaran Nair: On the origin of the mass gap for non-Abelian gauge theories in (2+1) dimensions, Phys.Lett. B 379 (1996) 141-147 [doi:10.1016/0370-2693(96)00422-4, arXiv:hep-th/9602155]

• Dimitra Karabali, Chanju Kim, V. Parameswaran Nair: Planar Yang-Mills theory: Hamiltonian, regulators and mass gap, Nucl. Phys. B 524 (1998) 661-694 [doi:10.1016/S0550-3213(98)00309-5, arXiv:hep-th/9705087]

• Dimitra Karabali, Chanju Kim, V. Parameswaran Nair: On the vacuum wavefunction and string tension of Yang-Mills theories in (2+1) dimensions, Phys. Lett. B 434 (1998) 103-109 [doi:10.1016/S0370-2693(98)00751-5, ]arXiv:hep-th/9804132]

Review:

• V. Parameswaran Nair: Yang-Mills theory in (2+1) dimensions: a short review, Nucl. Phys. Proc. Suppl. 108 (2002) 194-200 [doi:10.1016/S0920-5632(02)01328-2, arXiv:hep-th/0204063]

See also:

• Doug Pickrell: On $YM_2$ measures and area-preserving diffeomorphisms, Journal of Geometry and Physics 19 4 (1996) 315-367 [doi:10.1016/0393-0440(95)00034-8]

• Doug Pickrell: Notes on invariant measures for loop groups [arXiv:2207.09913]

Further discussion:

• Rocco Amorosso, Sergey Syritsyn, Raju Venugopalan: Entanglement Enabled Tomography of Flux Tubes in $(2+1)D$ Yang-Mills Theory [arXiv:2601.17199]