nLab D=6 supergravity

Contents

Context

Gravity

Super-Geometry

Contents

Idea

supergravity in dimension 6

Properties

U-duality

supergravity gauge group (split real form)T-duality group (via toroidal KK-compactification)U-dualitymaximal gauged supergravity
SL(2,)SL(2,\mathbb{R})1 SL ( 2 , ) SL(2,\mathbb{Z}) S-dualityD=10 type IIB supergravity
SL(2,)×(2,\mathbb{R}) \times O(1,1) 2\mathbb{Z}_2 SL ( 2 , ) SL(2,\mathbb{Z}) × 2\times \mathbb{Z}_2D=9 supergravity
SU(3)×\times SU(2)SL(3,)×SL(2,)(3,\mathbb{R}) \times SL(2,\mathbb{R})O(2,2;)O(2,2;\mathbb{Z})SL(3,)×SL(2,)SL(3,\mathbb{Z})\times SL(2,\mathbb{Z})D=8 supergravity
SU(5)SL(5,)SL(5,\mathbb{R})O(3,3;)O(3,3;\mathbb{Z})SL(5,)SL(5,\mathbb{Z})D=7 supergravity
Spin(10)Spin(5,5)Spin(5,5)O(4,4;)O(4,4;\mathbb{Z})O(5,5,)O(5,5,\mathbb{Z})D=6 supergravity
E₆E 6(6)E_{6(6)}O(5,5;)O(5,5;\mathbb{Z})E 6(6)()E_{6(6)}(\mathbb{Z})D=5 supergravity
E₇E 7(7)E_{7(7)}O(6,6;)O(6,6;\mathbb{Z})E 7(7)()E_{7(7)}(\mathbb{Z})D=4 supergravity
E₈E 8(8)E_{8(8)}O(7,7;)O(7,7;\mathbb{Z})E 8(8)()E_{8(8)}(\mathbb{Z})D=3 supergravity
E₉E 9(9)E_{9(9)}O(8,8;)O(8,8;\mathbb{Z})E 9(9)()E_{9(9)}(\mathbb{Z})D=2 supergravityE₈-equivariant elliptic cohomology
E₁₀E 10(10)E_{10(10)}O(9,9;)O(9,9;\mathbb{Z})E 10(10)()E_{10(10)}(\mathbb{Z})
E₁₁E 11(11)E_{11(11)}O(10,10;)O(10,10;\mathbb{Z})E 11(11)()E_{11(11)}(\mathbb{Z})

(Hull-Townsend 94, table 1, table 2)

References

General

Background on D=6D=6 spin representations and supersymmetry:

Formulation of D=6D=6 supergravity on superspace:

Further discussion:

For “exotic” 𝒩=(4,0)\mathcal{N} = (4,0)-supersymmetry:

Killing spinors

Discussion of Killing spinors/enhancement of number of supersymmetries in D=6 supergravity:

KK-reduction to JT gravity

Realization of JT-gravity as Kaluza-Klein reduction of D=6 supergravity on the worldvolume of D1-D5 brane bound states or M2-M5 brane bound states:

  • Yue-Zhou Li, Shou-Long Li, H. Lu, Exact Embeddings of JT Gravity in Strings and M-theory, Eur. Phys. J. C (2018) 78: 791 (arXiv:1804.09742)

  • Iosif Bena, Pierre Heidmann, David Turton, AdS 2AdS_2 Holography: Mind the Cap, JHEP 1812 (2018) 028 (arXiv:1806.02834)

Last revised on July 17, 2024 at 20:05:05. See the history of this page for a list of all contributions to it.