nLab Einstein-Yang-Mills-Dirac-Higgs theory

Idea

The theory in physics which describes the fundamental physics of the observable universe to best present knowledge is a local Lagrangian field theory which combines

theory:	Einstein-	Maxwell-	Yang-Mills-	Dirac-	Higgs
	gravity	electromagnetism	electroweak and strong nuclear force	fermionic matter	scalar field
fields	vielbein field $e$	$U(1)$-principal connection $\nabla_{em}$	$G$-principal connection	spinor $\psi$	scalar field $H$
Lagrangian $L =$	$R(e) vol(e) +$		$F_{\nabla_{}} \wedge \star_e F_{\nabla_{}} +$	$(\psi , D \psi) vol(e) +$	$\nabla \bar H \wedge \star_e \nabla H + \left(\lambda {\vert H\vert}^4 - \mu^2 {\vert H\vert}^2 \right) vol(e)$

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

• Einstein-Hilbert action

• Einstein-Maxwell theory

• standard model of particle physics

• standard model of cosmology

References

Section Prequantum gauge theory and Gravity in

• geometry of physics

On Yang-Mills monopoles:

• K. Lee, V. P. Nair, Erick J. Weinberg, Black Holes in Magnetic Monopoles, Phys. Rev. D45 (1992) 2751-2761 (arXiv:hep-th/9112008)

• H. W. Braden, V. Varela, Solutions for Einstein-Yang-Mills-Dilaton- σ Models, Phys. Rev. D58:124020, 1998 (arXiv:hep-th/9804204)

• Betti Hartmann, Burkhard Kleihaus, Jutta Kunz, Axially Symmetric Monopoles and Black Holes in Einstein-Yang-Mills-Higgs Theory, Phys. Rev. D65 (2002) 024027 (arXiv:hep-th/0108129)