Six-dimensional Type Research Articles

Non-Kähler SYZ Mirror Symmetry

We study SYZ mirror symmetry in the context of non-Kaehler Calabi-Yau manifolds. In particular, we study the six-dimensional Type II supersymmetric $SU(3)$ systems with Ramond-Ramond fluxes, and generalize them to higher dimensions. We show that Fourier-Mukai transform provides the mirror map between these Type IIA and Type IIB supersymmetric systems in the semi-flat setting. This is concretely exhibited by nilmanifolds.

Holographic entropy and Calabi’s diastasis

The entanglement entropy for interfaces and junctions of two-dimensional CFTs is evaluated on holographically dual half-BPS solutions to six-dimensional Type 4b supergravity with m anti-symmetric tensor supermultiplets. It is shown that the moduli space for an N-junction solution projects to N points in the Kaehler manifold SO(2,m)/( SO(2) x SO(m)). For N=2 the interface entropy is expressed in terms of the central charge and Calabi's diastasis function on SO(2,m)/(SO(2) x SO(m)), thereby lending support from holography to a proposal of Bachas, Brunner, Douglas, and Rastelli. For N=3, the entanglement entropy for a 3-junction decomposes into a sum of diastasis functions between pairs, weighed by combinations of the three central charges, provided the flux charges are all parallel to one another or, more generally, provided the space of flux charges is orthogonal to the space of unattracted scalars. Under similar assumptions for N>3, the entanglement entropy for the N-junction solves a variational problem whose data consist of the N central charges, and the diastasis function evaluated between pairs of N asymptotic AdS_3 x S^3 regions.

Attractor horizons in six-dimensional type IIB supergravity

We consider near horizon geometries of extremal black holes in six-dimensional type IIB supergravity. In particular, we use the entropy function formalism to compute the charges and thermodynamic entropy of these solutions. We also comment on the role of attractor mechanism in understanding the entropy of the Hopf T-dual solutions in type IIA supergravity.

Simple holographic duals to boundary CFTs

By relaxing the regularity conditions imposed in arXiv:1107.1722 on half-BPS solutions to six-dimensional Type 4b supergravity, we enlarge the space of solutions to include two new half-BPS configurations, which we refer to as the AdS2-cap and the AdS2-funnel. We give evidence that the AdS2-cap and AdS2-funnel can be interpreted as fully back-reacted brane solutions with respectively AdS2 and AdS2 × S 2 world volumes. AdS2-cap and AdS2-funnel solutions with a single asymptotic AdS3 × S 3 region are constructed analytically. We argue that AdS2-cap solutions provide simple examples of holographic duals to boundary CFTs in two dimensions and present calculations of their holographic boundary entropy to support the BCFT dual picture.

Engineering of Quantum Hall Effect from type IIA string theory on the K3 surface

Using D-brane configurations on the K3 surface, we give six-dimensional type IIA stringy realizations of the Quantum Hall Effect (QHE) in 1+2 dimensions. Based on the vertical and horizontal lines of the K3 Hodge diamond, we engineer two different stringy realizations. The vertical line presents a realization in terms of D2 and D6-branes wrapping the K3 surface. The horizontal one is associated with hierarchical stringy descriptions obtained from a quiver gauge theory living on a stack of D4-branes wrapping intersecting 2-spheres embedded in the K3 surface with deformed singularities. These geometries are classified by three kinds of the Kac–Moody algebras: ordinary, i.e. finite dimensional, affine and indefinite. We find that no stringy QHE in 1+2 dimensions can occur in the quiver gauge theory living on intersecting 2-spheres arranged as affine Dynkin diagrams. Stringy realizations of QHE can be done only for the finite and indefinite geometries. In particular, the finite Lie algebras give models with fractional filling fractions, while the indefinite ones classify models with negative filling fractions which can be associated with the physics of holes in the graphene.