Spinorial geometry and Killing spinor equations of 6D supergravity

M Akyol , G Papadopoulos (1)

1 AEI - Max-Planck-Institut für Gravitationsphysik ( Albert-Einstein-Institut )

We solve the Killing spinor equations of 6-dimensional (1, 0)-supergravity coupled to any number of tensor, vector and scalar multiplets in all cases. The isotropy groups of Killing spinors are Sp(1)*Sp(1)H(1), U (1)*Sp(1)H(2), Sp(1)H(3, 4), Sp(1)(2), U (1)(4) and {1}(8), where in parenthesis is the number of supersymmetries preserved in each case. If the isotropy group is non-compact, the spacetime admits a parallel null 1-form with respect to a connection with torsion the 3-form field strength of the gravitational multiplet. The associated vector field is Killing and the 3-form is determined in terms of the geometry of spacetime. The Sp(1)  H case admits a descendant solution preserving 3 out of 4 supersymmetries due to the hyperini Killing spinor equation. If the isotropy group is compact, the spacetime admits a natural frame constructed from 1-form spinor bi-linears. In the Sp(1) and U (1) cases, the spacetime admits 3 and 4 parallel 1-forms with respect to the connection with torsion, respectively. The associated vector fields are Killing and under some additional restrictions the spacetime is a principal bundle with fibre a Lorentzian Lie group. The conditions imposed by the Killing spinor equations on all other fields are also determined.

Mots clés: Physical Sciences

Domaines: Relativité Générale et Cosmologie Quantique [gr-qc]

M Akyol, G Papadopoulos. Spinorial geometry and Killing spinor equations of 6D supergravity. Classical and Quantum Gravity, 2011, 28 (10), pp.105001. ⟨10.1088/0264-9381/28/10/105001⟩. ⟨hal-00699367⟩