Related papers: M-theory, exceptional generalised geometry and sup…
The recent investigation of the gauge structure of extended geometry is generalised to situations when ancillary transformations appear in the commutator of two generalised diffeomorphisms. The relevant underlying algebraic structure turns…
We study the physics of globally consistent four-dimensional $\mathcal{N}=1$ supersymmetric M-theory compactifications on $G_2$ manifolds constructed via twisted connected sum; there are now perhaps fifty million examples of these…
We explore geometries that give rise to a novel algebraic structure, the Exceptional Drinfeld Algebra, which has recently been proposed as an approach to study generalised U-dualities, similar to the non-Abelian and Poisson-Lie…
It is shown that Electromagnetism creates geometry different from Riemannian geometry. General geometry including Riemannian geometry as a special case is constructed. It is proven that the most simplest special case of General Geometry is…
In these lectures we review Generalized Complex Geometry and discuss two main applications to string theory: the description of supersymmetric flux compactifications and the supersymmetric embedding of D-branes. We start by reviewing…
A geometric formulation which describes extended supergravities in any dimension in presence of electric and magnetic sources is presented. In this framework the underlying duality symmetries of the theories are manifest. Particular…
We analyse the 4-dimensional effective supergravity theories obtained from the Scherk--Schwarz reduction of M-theory on twisted 7-tori in the presence of 4-form fluxes. We implement the appropriate orbifold projection that preserves a…
This thesis analyses gauged supergravities in various dimensions and their possible origin from compactifications of string theory. In the effective description the fluxes appear in the theory as deformation parameters generating a…
We show how to construct half-maximal consistent truncations of 10- and 11-dimensional supergravity to seven dimensions using exceptional field theory. This procedure gives rise to a seven-dimensional half-maximal gauged supergravity…
We present a systematic framework for constructing consistent truncations of supergravity based on exceptional generalized cosets of the form $\GS \backslash G/H$. This approach generalizes the well-established generalized Scherk-Schwarz…
Ten-dimensional type II supergravity can be reformulated as a generalised geometrical analogue of Einstein gravity, defined by an $O(9,1)\times O(1,9)\subset O(10,10)\times\mathbb{R}^+$ structure on the generalised tangent space. To leading…
In this paper we generalize special geometry to arbitrary signatures in target space. We formulate the definitions in a precise mathematical setting and give a translation to the coordinate formalism used in physics. For the projective…
Weinberg-Salam theory and $SU(5)$ grand unified theory are reconstructed using the generalized differential calculus extended on the discrete space $M_4\times Z_{\mathop{}_{N}}$. Our starting point is the generalized gauge field expressed…
Generalized complex geometry, as developed by Hitchin, contains complex and symplectic geometry as its extremal special cases. In this thesis, we explore novel phenomena exhibited by this geometry, such as the natural action of a B-field.…
All maximal supergravities in four space-time dimensions are presented. The ungauged Lagrangians can be encoded in an E_7(7)\Sp(56,R)/GL(28) matrix associated with the freedom of performing electric/magnetic duality transformations. The…
This paper introduces a geometric representation of hypergraphs by representing hyperedges as simplices. Building on this framework, we employ homotopy groups to analyze the topological structure of hypergraphs embedded in high-dimensional…
A family of geometries on S^7 arise as solutions of the classical equations of motion in 11 dimensions. In addition to the conventional riemannian geometry and the two exceptional Cartan-Schouten compact flat geometries with torsion, one…
In this paper we continue our program, started in [2], of building up explicit generalized Euler angle parameterizations for all exceptional compact Lie groups. Here we solve the problem for E7, by first providing explicit matrix…
The maximal supergravity theory in three dimensions, which has local SO(16) and rigid $E_8$ symmetries, is discussed in a superspace setting starting from an off-shell superconformal structure. The on-shell theory is obtained by imposing…
The main topic of this thesis are flux compactifications. Firstly, we study dimensional reductions of type II and eleven-dimensional supergravities using exceptional generalised geometry. We start by presenting the needed mathematical…