Contents

# Contents

## Properties

### Equations of motion from the Bianchi identity

The equations of motion of 10d super Yang-Mills happen to be equivalent in superspace to the Bianchi identity

$D F = 0$

subject to the constraint that the bispinorial part of the curvature 2-form vanishes

$F_{\alpha \beta} = 0$

After embedding into heterotic supergravity this becomes parts of the torsion constraints of supergravity. See there.

In this superspace formulation the gaugino $\chi$ appears as the even-odd component of the super-curvature form

(1)$F_{(1,1)} \;\propto\; \left(\overline{\psi} \Gamma_a \chi\right) \wedge e^a$

(where $(e^a, \psi^\alpha)$ is the super vielbein). This is (Witten 86 (8), Bonora-Pasti-Tonin 87, below (11), Bonora-Bregola-Lechner-Pasti-Tonin 87, (2.27)).

### Compactification to the point

The KK-compactification of $D=10$ super-Yang-Mills to the point is a theory whose fields are simply elements of the gauge Lie algebra, hence matrices if we have a matrix Lie algebra. The theory defined by this reduction is called the IKKT matrix model.

## References

Last revised on July 11, 2019 at 12:38:13. See the history of this page for a list of all contributions to it.