nLab
graviphoton

Contents

Contents

Idea

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

Definition

If v 5Γ(TX^)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 X^\widehat X bundle is the contraction of the metric tensor g^\widehat g with this vector field:

Ag^(v,). 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 1C_1 of type IIA string theory.

On D4-branes

The graviphoton as the RR-field potential C 1C_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:

L D4 WZC 1FF. \mathbf{L}_{D4}^{WZ} \;\propto\; C_1 \wedge \langle F \wedge F\rangle \,.

References

General

See also

In string theory

The graviphoton of the duality between M-theory and type IIA string theory, as the RR-field-potential C 1C_1 in the higher WZW term of the D4-brane:

For more see at Green-Schwarz sigma model – References – For D-branes.

Discussion as the theta angle of the Witten-Sakai-Sugimoto model for QCD on D4-branes:

  • Si-wen Li, around (3.1) of The theta-dependent Yang-Mills theory at finite temperature in a holographic description (arXiv:1907.10277)

Last revised on July 25, 2019 at 10:07:12. See the history of this page for a list of all contributions to it.