Abstract
Admissible curved space backgrounds for four-dimensional supersymmetric field theories are determined by solving Killing spinor equations of four-dimensional off-shell supergravities. These can be obtained by combining ten-dimensional type IIB supersymmetry with D-brane kappa-symmetry and identifying auxiliary fields of the four-dimensional supergravity fields in terms of type IIB fields. In this paper we show how to extend a number of solutions of four-dimensional Killing spinor equations with four or less supercharges to solutions of the ten-dimensional supersymmetry constraints.
Highlights
In [10] it was shown how backgrounds which simultaneously obey the supersymmetry conditions for bulk type IIB theory and D3-branes imply the vanishing of the gravitino variation of a four-dimensional N = 1 off-shell supergravity.1 the four-dimensional supergravity appearing here is the so-called 16/16 formulation [13,14,15], and can be thought of either as old minimal supergravity coupled to a vector multiplet or new minimal supergravity coupled to a chiral multiplet
These can be obtained by combining ten-dimensional type IIB supersymmetry with D-brane kappa-symmetry and identifying auxiliary fields of the four-dimensional supergravity fields in terms of type IIB fields
In this paper we show how to extend a number of solutions of four-dimensional Killing spinor equations with four or less supercharges to solutions of the ten-dimensional supersymmetry constraints
Summary
In order to determine which manifolds can support globally supersymmetric field theories, a number of four-dimensional equations need to be solved. A second possibility is to relax the D3-brane κ-symmetry conditions by introducing a suitable additional component ε− in the Killing spinor satisfying Γ0ε− = −ε−.7 This can be interpreted as either corresponding to the presence of non-linear supersymmetry and intstantons (see [12]), or as a near-horizon approximation background. The ten-dimensional external gravitino supersymmetry conditions are precisely of the form of the Killing spinor equations imposed by the vanishing of the gravitino of 16/16 supergravity. Unlike the external gravitino and modified dilatino equations, the internal gravitino equation has no four-dimensional interpretation Instead, it should be considered as additional constraints imposed by demanding that a four-dimensional background dictated by the 16/16 supersymmetry conditions can be supersymmetrically embedded into a tendimensional background
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