# nLab Einstein-Yang-Mills theory

### Context

#### Gravity

gravity, supergravity

## Quantum theory

#### Differential cohomology

differential cohomology

# Contents

## Idea

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,

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

where

standard model of particle physics and cosmology

theory:Einstein-Yang-Mills-Dirac-Higgs
gravityelectroweak and strong nuclear forcefermionic matterscalar field
field content:vielbein field $e$principal connection $\nabla$spinor $\psi$scalar field $H$
Lagrangian:scalar curvature densityfield strength squaredDirac operator component densityfield strength squared + potential density
$L =$$R(e) vol(e) +$$\langle F_\nabla \wedge \star_e F_\nabla\rangle +$$(\psi , D_{(e,\nabla)} \psi) vol(e) +$$\nabla \bar H \wedge \star_e \nabla H + \left(\lambda {\vert H\vert}^4 - \mu^2 {\vert H\vert}^2 \right) vol(e)$

## References

Section Prequantum gauge theory and Gravity in

Revised on September 20, 2016 00:22:18 by Urs Schreiber (89.204.137.119)