Georgios Papadopoulos

M2-branes, 3-Lie algebras and Plücker relations

We find that the structure constants 4-form of a metric 3-Lie algebra is the sum of the volume forms of orthogonal 4-planes proving a conjecture in math/0211170. In particular, there is no metric 3-Lie algebra associated to a (N) Lie algebra for N>2. We examine the implication of this result on the existence of a multiple M2-brane theory based on metric 3-Lie algebras.

Spinorial geometry, horizons and superconformal symmetry in six dimensions

The spinorial geometry method of solving Killing spinor equations is reviewed as it applies to six-dimensional (1,0) supergravity. In particular, it is explained how the method is used to identify both the fractions of supersymmetry preserved by and the geometry of all supersymmetric backgrounds. Then two applications are described to systems that exhibit superconformal symmetry. The first is the proof that some six-dimensional black hole horizons are locally isometric to AdS3 × Σ3, where Σ3 is diffeomeorphic to S3. The second one is a description of all supersymmetric solutions of six-dimensional (1,0) superconformal theories and in particular of their brane solitons.

On the structure of k-Lie algebras

We show that the structure constants of k-Lie algebras, k > 3, with a positive definite metric are the sum of the volume forms of orthogonal k-planes. This generalizes the result for k = 3 in Papadopoulos (2008 Preprint arXiv:0804.2662) and Gauntlett and Gutowski (2008 Preprint arXiv:0804.3078), and confirms a conjecture in Figueroa-OFarrill and Papadopoulos (2002 Preprint math/0211170).

Seeking the balance: patching double and exceptional field theories

A bstractWe investigate the patching of double and exceptional field theories. In double field theory the patching conditions imposed on the spacetime after solving the strong section condition imply that the 3-form field strength H is exact. A similar conclusion can be reached for the form field strengths of exceptional field theories after some plausive assumptions are made on the relation between the transition functions of the additional coordinates and the patching data of the form field strengths. We illustrate the issues that arise, and explore several alternative options which include the introduction of C-folds and of the topological geometrisation condition.

Heterotic Black Horizons

We show that the supersymmetric near horizon geometry of heterotic black holes is either an AdS3 fibration over a 7-dimensional manifold which admits a G2 structure compatible with a connection with skew-symmetric torsion, or it is a product

New half supersymmetric solutions of the heterotic string

{mathbb{R}^{1,1}} times {mathcal{S}^8}

(1,0) superconformal theories in six dimensions and Killing spinor equations

, where

Supersymmetry of AdS and flat backgrounds in M-theory

{mathcal{S}^8}

Killing-Yano equations and G structures

is a holonomy Spin(7) manifold, preserving 2 and 1 supersymmetries respectively. Moreover, we demonstrate that the AdS3 class of heterotic horizons can preserve 4, 6 and 8 supersymmetries provided that the geometry of the base space is further restricted. Similarly

Supersymmetry of IIA warped flux AdS and flat backgrounds

{mathbb{R}^{1,1}} times {mathcal{S}^8}