nLab
D=7 supergravity

Context

Gravity

Physics

physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes


theory (physics), model (physics)

experiment, measurement, computable physics

Super-Geometry

Contents

Idea

Reductions of 11-dimensional supergravity on a 4-dimensional space to a 7-dimensional theory.

Properties

U-duality

Maximal 7d supergravity has SL(5,)SL(5,\mathbb{Z})-U-duality (Kumar-Vafa 96, section 3.4, Rozali 97).

Holography

The AdS7/CFT6-correspondence relates 7-dimensional supergravity on asymptocially 7d anti de Sitter spacetimes to the 6d (2,0)-superconformal QFT.

References

General

The maximally N=4 supersymmetric SO(5)SO(5)-gauged supergravity in 7-dimensions was first constructed in

There are also gaugings for non-compact groups

The N=2 Sp(1)-gauged theory was described in

See also

Discussion of AdS vacua:

Heterotic 7d supergravity

By reduction from 10d/11d supergravity

The following references discuss construction of full 7d sugra theories or of their solutions by KK-reduction from 11-dimensional supergravity or from 10d type II supergravity.

The construction of 7d supergravity by KK-reduction from 11-dimensional supergravity was first indicated in

via what is now called Freund-Rubin compactification.

That their Ansatz is indeed consistent has been shown in

The SL(5,)SL(5,\mathbb{Z})-U-duality in 7d is discussed in

Explicit compactifications are discussed in

See also

Relation to massive type IIA supergravity and bound states of D-branes:

D’Auria-Fré formulation of supergravity

Discussion in the D'Auria-Fré formulation of supergravity is in

and the 7d analog of the DF-algebra (the Chevalley-Eilenberg algebra of a spinorial extension of the M-theory super Lie algebra) is due to