Contents

# Contents

## Idea

Given a Kaluza-Klein compactification on a circle principal bundle $(\widehat X, \widehat g)$, the graviphoton field is the resulting gauge field (electromagnetic field) on the base of the fibration.

## Definition

If $v_5 \in \Gamma\big( T\widehat X\big)$ denotes the vertical vector field which corresponds to the isometric flow along the circle fibers, the graviphoton field, regraded as a Cartan connection differential 1-form on the total space $\widehat X$ bundle is the contraction of the metric tensor $\widehat g$ with this vector field:

$A \;\coloneqq\; \widehat g(v,-) \,.$

## Examples

### In type IIA string theory

In the duality between M-theory and type IIA string theory, the graviphoton of the KK-compactification is the RR-field potential $C_1$ of type IIA string theory.

### On D4-branes

The graviphoton as the RR-field potential $C_1$ of type IIA string theory then appears in the higher WZW term on the D4-brane (CGNSW 96 (7.4) APPS97b (51)) as the theta angle in D=5 super Yang-Mills theory:

$\mathbf{L}_{D4}^{WZ} \;\propto\; C_1 \wedge \langle F \wedge F\rangle \,.$

## References

### General

The graviphoton of the duality between M-theory and type IIA string theory, as the RR-field-potential $C_1$ in the higher WZW term of the D4-brane: