nLab Einstein-Yang-Mills theory




Differential cohomology


physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes

theory (physics), model (physics)

experiment, measurement, computable physics



What is called Einstein-Yang-Mills theory in physics is the theory/model (in theoretical physics) describing gravity together with Yang-Mills fields such as the electroweak field or the strong nuclear force of quantum chromodynamics. For the special case that the gauge group is the circle group this reproduces Einstein-Maxwell theory.

Einstein-Yang-Mills theory is a local Lagrangian field theory defined by the action functional which is the Einstein-Hilbert action plus the Yang-Mills action functional involving the given metric,

S G+YM:(e,) XR(e)vol(e)+ XF eF , S_{G+YM} \; \colon \; (e, \nabla) \mapsto \int_{X} R(e) vol(e) + \int_X \langle F_\nabla \wedge \star_e F_\nabla\rangle \,,


standard model of particle physics and cosmology

gravityelectroweak and strong nuclear forcefermionic matterscalar field
field content:vielbein field eeprincipal connection \nablaspinor ψ\psiscalar field HH
Lagrangian:scalar curvature densityfield strength squaredDirac operator component densityfield strength squared + potential density
L=L = R(e)vol(e)+R(e) vol(e) + F eF +\langle F_\nabla \wedge \star_e F_\nabla\rangle + (ψ,D (e,)ψ)vol(e)+ (\psi , D_{(e,\nabla)} \psi) vol(e) + H¯ eH+(λ|H| 4μ 2|H| 2)vol(e) \nabla \bar H \wedge \star_e \nabla H + \left(\lambda {\vert H\vert}^4 - \mu^2 {\vert H\vert}^2 \right) vol(e)


Section Prequantum gauge theory and Gravity in

On Yang-Mills monopoles:

  • J. Bjoraker, Y. Hosotani, Monopoles, Dyons and Black Holes in the Four-Dimensional Einstein-Yang-Mills Theory, Phys. Rev. D62:043513, 2000 (arXiv:hep-th/0002098)

Last revised on August 7, 2021 at 19:52:38. See the history of this page for a list of all contributions to it.