# nLab gravity

Contents

### Context

#### Gravity

gravity, supergravity

# Contents

## Idea

A field configuration of the physical theory of gravity on a spacetime $X$ is equivalently

(This parameterization of the gravitational field is called the first-order formulation of gravity.) The component $E$ of the connection is the vielbein that encodes a pseudo-Riemannian metric $g = E \cdot E$ on $X$ and makes $X$ a pseudo-Riemannian manifold. Its quanta are the gravitons.

The non-propagating field? $\Omega$ is the spin connection.

The action functional on the space of such connection which defines the classical field theory of gravity is the Einstein-Hilbert action.

More generally, supergravity is a gauge theory over a supermanifold $X$ for the super Poincare group. The field of supergravity is a Lie-algebra valued form with values in the super Poincare Lie algebra.

$(E,\Omega, \Psi) : T X \to \mathfrak{siso}(d-1,1)$

The additional fermionic field $\Psi$ is the gravitino field.

So the configuration space of gravity on some $X$ is essentially the moduli space of Riemannian metrics on $X$.

## Details

for the moment see D'Auria-Fre formulation of supergravity for further details

## References

### General

Textbooks include

Lecture notes

The theory of gravity based on the standard Einstein-Hilbert action may be regarded as just an effective quantum field theory, which makes some of its notorious problems be non-problems:

### Covariant phase space

The (reduced) covariant phase space of gravity (presented for instance by its BV-BRST complex, see there fore more details) is discussed for instance in

which is surveyed in

• Katarzyna Rejzner, The BV formalism applied to classical gravity (pdf)

Careful discussion of observables in gravity is in

### Non-renormalizability

The result that gravity is not renormalizable is due to

Review includes

Last revised on January 24, 2019 at 06:06:02. See the history of this page for a list of all contributions to it.