Generalised G₂-structures and type IIB superstrings

Abstract

The recent mathematical literature introduces generalised geometries which are defined by a reduction from the structure group SO(d, d) of the vector bundle T d ⊕ T d * to a special subgroup. In this article we show that compactification of IIB superstring vacua on 7manifolds with two covariantly constant spinors leads to a generalised G 2 -structure associated with a reduction from SO(7, 7) to G 2 ×G 2 . We also consider compactifications on 6-manifolds where analogously we obtain a generalised SU (3)-structure associated with SU (3) × SU (3), and show how these relate to generalised G 2 -structures.

Enhanced supersymmetry from vanishing Euler number

“…so that 14) which is clearly nowhere vanishing. The one-forms v i span the two-dimensional component T * 2 Y of T * Y at each point over the base Y .…”

“…The last equation determines the symmetric part of T I jK η KJ , j = 1, 2, so that 14) whereT I jK is a pair of so(3, n − 3) matrices, i.e.…”

$ \mathcal{N} = 1 $ vacua in exceptional generalized geometry

“…Supersymmetry conditions in the presence of H-flux amount precisely to H-twisting the generalized Calabi-Yau metric condition (4.9). More precisely, vacua preserving fourdimensional N = 2 supersymmetry in the presence of NS fluxes should satisfy [15] …”

Black hole attractors and pure spinors

“…the appendix of [35]. Recently, this fact has been used in the context of generalized complex geometry [9,[16][17][18].…”

“…These pure spinors play a central role in the theory of generalized complex manifolds [14][15][16], and have recently found several applications in supergravity, in the study of compactifications on six [9,17,18] and seven [18,19] dimen-sional manifolds. We give a brief introduction to pure spinors in appendix B.…”