Yang-Mills as massive Chern-Simons theory: a third way to three-dimensional gauge theories

Abstract

The Yang-Mills (YM) equation in three spacetime dimensions (3D) can be modified to include a novel parity-preserving interaction term, with inverse mass parameter, in addition to a possible topological mass term. The novelty is that the modified YM equation is not the Euler-Lagrange equation of any gauge-invariant local action for the YM gauge potential alone. Instead, consistency is achieved in the "third way" exploited by 3D "minimal massive gravity". We relate our results to the "novel Higgs mechanism" for Chern-Simons gauge theories.

arXiv comment5 pages. New title in v.2 to accord with published version. Also includes minor corrections and two additional paragraphs

References in corpus (9)

• M2 to D2
• The gauge dual of Romans mass
• Minimal Massive 3D Gravity
• Multiple Membranes in M-theory
• Matter coupling in 3D "Minimal Massive Gravity"
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• Unravelling the novel Higgs mechanism in (2+1)d Chern-Simons theories
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Cited by in corpus (13)

• Exotic Massive 3D Gravity
• The Third Way to 3D Gravity
• Exotic massive 3D gravities from truncation
• The Third Way to Interacting $p$-form Theories
• On-shell versus Off-shell Equivalence in 3D Gravity
• The Third way to 3D Supersymmetric Massive Yang-Mills Theory
• A note on the third way consistent deformation of Yang-Mills theory
• A Review of Third Way Consistent Theories
• Three-dimensional $\mathrm{SL}(2,\mathbb{R})$ Yang-Mills theory is three-dimensional gravity with background sources
• Gravity from AKSZ-Manin theories in two, three, and four dimensions
• Perturbative Unitarity Calls for An Action
• Homotopy Manin Theories: Generalising Third-Way, Yang-Mills and Integrable Sigma Models
• Ersatz gravity and black-hole thermodynamics from Manin gauge theory with noncompact gauge group