Related papers: Complex Structures, T-duality and Worldsheet Insta…

In this work a thorough study of a number of specific supersymmetric sigma-models with extended supersymmetry is performed within the context of generalised complex geometry. More specifically the supersymmetric Wess-Zumino-Witten model on…

We take a fresh look at the relation between generalised K\"ahler geometry and $N=(2,2)$ supersymmetric sigma models in two dimensions formulated in terms of $(2,2)$ superfields. Dual formulations in terms of different kinds of superfield…

The doubled formulation of string theory, which is T-duality covariant and enlarges spacetime with extra coordinates conjugate to winding number, is reformulated and its geometric and topological features examined. It is used to formulate…

I stress how the form of sigma models with (2, 2) supersymmetry differs depending on the number of manifest supersymmetries. The differences correspond to different aspects/formulations of Generalized K\"ahler Geometry.

Given a conical affine special K\"{a}hler (CASK) manifold together with a compatible mutually local variation of BPS structures, one can construct a quaternionic-K\"{a}hler (QK) manifold. We call the resulting QK manifold an instanton…

We revisit the backgrounds of type IIB on manifolds with $SU(4)$-structure and discuss two sets of solutions arising from internal geometries that are complex and symplectic respectively. Both can be realized in terms of generalized complex…

In this paper we propose and investigate in full generality new notions of (continuous, non-isometric) symmetry on hyperk\"ahler spaces. These can be grouped into two categories, corresponding to the two basic types of continuous…

We consider and resolve the gap problem for almost quaternion-Hermitian structures, i.e. we determine the maximal and submaximal symmetry dimensions, both for Lie algebras and Lie groups, in the class of almost quaternion-Hermitian…

A description of the fundamental degrees of freedom underlying generalized K\"ahler geometry, which separates its holomorphic moduli from its compatible Riemannian metric in a similar way to the K\"ahler case, has been sought since its…

We study dualities between classes of relational topological structures, given by Hom-functors. We show that there exists a 2-element structure with infinitely many relations, which reconstructs all other structures generated by a 2-element…

We use newly discovered N = (2, 2) vector multiplets to clarify T-dualities for generalized Kahler geometries. Following the usual procedure, we gauge isometries of nonlinear sigma-models and introduce Lagrange multipliers that constrain…

A hyperk\"ahler manifold is defined as a Riemannian manifold endowed with three covariantly constant complex structures that are quaternionically related. A twistor space is characterized as a holomorphic fiber bundle $p: \mathcal{Z}…

We study generalized Kahler structures on N = (2, 2) supersymmetric Wess-Zumino-Witten models; we use the well known case of SU(2) x U(1) as a toy model and develop tools that allow us to construct the superspace action and uncover the…

Building from ideas of hypercomplex analysis on the quaternionic unit ball, we introduce Hermitian, Riemannian and K\"ahler-like structures on the latter. These are built from the so-called regular M\"obius transformations. Such geometric…

We introduce the notion of even Clifford structures on Riemannian manifolds, a framework generalizing almost Hermitian and quaternion-Hermitian geometries. We give the complete classification of manifolds carrying parallel even Clifford…

Heterotic supergravity with (1+3)--dimensional domain wall configurations and (warped) internal, six dimensional, almost-K\"ahler manifolds $\ ^6\mathbf{X}$ are studied. Considering ten dimensional spacetimes with nonholonomic distributions…

We construct the explicit form of three almost complex structures that a Riemannian manifold with self-dual curvature admits and show that their Nijenhuis tensors vanish so that they are integrable. This proves that gravitational instantons…

Clifford geometric algebras of multivectors are introduced which exhibit a bilinear form which is not necessarily symmetric. Looking at a subset of bi-vectors in CL(K^{2n},B), we proof that theses elements generate the Hecke algebra…

Let M be a hyperk\"ahler manifold. The S^2-family of complex structures compatible with the hyperk\"ahler metric can be assembled into a single complex structure on Z=MxS^2; the resulting complex manifold is known as the twistor space of M.…

In this paper, we study the geometries given by commuting pairs of generalized endomorphisms ${\cal A} \in \text{End}(T\oplus T^*)$ with the property that their product defines a generalized metric. There are four types of such commuting…