4-dimensional supergravity




physics, mathematical physics, philosophy of physics

Surveys, textbooks and lecture notes

theory (physics), model (physics)

experiment, measurement, computable physics




supergravity in dimension 4.

The maximally supersymmetric N=8N = 8-version arises from type II supergravity in 10 dimension by compactification on a 6-torus.

The N=1N=1-version arises from KK-reduction via M-theory on G2-manifolds. This hosts the super 2-brane in 4d.


On N=8N=8 d=4d=4 supergravity

On N=1N=1 d=4d = 4 supergravity

There are two different off-shell formulations, the “old minimal”

and the “new minimal” supergravity

  • V. Akulov, D. Volkov and V. Soroka, Theor. Math. Phys. 31 (1977) 285; M.F. Sohnius and P.C. West, idem. Phys. Lett. 105B (1981) 353; idem. Nucl. Phys. B198 (1982) 493.

  • M.F. Sohnius and P.C. West, `The New Minimal Formulation of N = 1 Supergravity and its Tensor Calculus', Nueld Workshop, 1981:0187 (London, England, Aug. 1981).

  • Jim Gates, M. Rocek and Warren Siegel, Nucl. Phys. B198 (1982) 113

These two versions were later understood to be two different gauge fixings of N=1 d=4 coformal supergravity. Yet other gauge fixings are discussed in

  • Jim Gates, Jr., Hitoshi Nishino, Will the Real 4D, N=1N=1 SG Limit of Superstring/M-Theory Please Stand Up?, Phys.Lett.B492:178-186,2000 (arXiv:hep-th/0008206)

See also

  • Nicolas Boulanger, Mboyo Esole, A Note on the uniqueness of D=4D = 4, N=1N=1 supergravity, Class.Quant.Grav. 19 (2002) 2107-2124 (arXiv:gr-qc/0110072)

Textbook accounts include

Survey includes


Discussion of gauged supergravity in 4d originates around

(where the E7-U-duality group was first seen)

Evidence for perturbative finiteness of N=8N=8 4d SuGra is discussed in

surveyed in

See also

Lift to string theory and M-theory

Discussion of lifts of gauged 4d supergravity to string theory/M-theory includes

Revised on December 21, 2015 06:57:39 by Urs Schreiber (