# 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

| | gravity | electroweak and strong nuclear force | fermionic matter | scalar field | | field content: | vielbein field $e$ | principal connection $\nabla$ | spinor $\psi$ | scalar field $H$ | | Lagrangian: | scalar curvature density | field strength squared | Dirac operator component density | field 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 January 14, 2013 18:21:35 by Urs Schreiber (203.116.137.162)