Supersymmetric D-branes and calibrations on general Script N = 1 backgrounds

Abstract

We study the conditions to have supersymmetric D-branes on general N = 1 backgrounds with Ramond-Ramond fluxes. These conditions can be written in terms of the two pure spinors associated to the SU (3) × SU (3) structure on T M ⊕ T ⋆ M , and can be split into two parts each involving a different pure spinor. The first involves the integrable pure spinor and requires the D-brane to wrap a generalised complex submanifold with respect to the generalised complex structure associated to it. The second contains the non-integrable pure spinor and is related to the stability of the brane. The two conditions can be rephrased as a generalised calibration condition for the brane. The results preserve the generalised mirror symmetry relating the type IIA and IIB backgrounds considered, giving further evidence for this duality.

Holographic flows in non-Abelian T-dual geometries

“…Indeed calibrated smeared sources, were not JHEP11(2015)212 considered in [20]. An extended G-structure derivation would be a necessary step to prove that non-Abelian T-duality is a solution generating technique for supersymmetric R 1,3 ×M 6 in the presence of such sources, using the results of [83,84]. It is likely that the criteria for SUSY to be preserved is the existence of a set of N = 1 pure spinors Ψ ± supported by the seed solution that are independent of the SU(2) coordinates in the frames of eq.…”

New N $$ \mathcal{N} $$ =1 supersymmetric AdS 5 backgrounds in type IIA supergravity

“…The Gravitino and Dilatino supergravity equations then can be restated as 1 Notice that Killing spinor also has a vanishing derivative along the U(1)α isometry so a SUSY preserving Abelian T-duality can be performed here, indeed that was part of the duality chain in [6,7] that led to the discovery of these Y p,q geometries. 2 Our conventions essentially follow those of [37] as used in [19] where further details of the action of non-Abelian T-duality on G-structures can be found.…”

On D-brane moduli stabilisation

“…In order to preserve supersymmetry, the (backreacted) sources must be calibrated [57,58]. This means that they should wrap generalised complex submanifolds, i.e.…”