Related papers: Geometric algebra techniques in flux compactificat…
G-structure techniques are used to construct broad classes of circle compactifications of Mink$_{D+1}$ solutions to Mink$_{D}$ embedded into type II supergravity for $D=1,...5$. Under a certain assumptions we show that the conditions that…
We consider the bosonic sectors of supergravity theories in ten and eleven dimensions which correspond to the low energy limits of string theories and M-theory. The solutions of supergravity field equations are known as supergravity…
Complimentary geometric and non-geometric consistent reductions of IIB supergravity are studied. The geometric reductions on the identified group manifold X are found to have a gauge symmetry with Lie algebroid structure, generalising that…
Extreme near-horizon geometries in D=11 supergravity preserving four supersymmetries are classified. It is shown that the Killing spinors fall into three possible orbits, corresponding to pairs of spinors defined on the spatial…
We investigate the Killing spinor equations of IIB supergravity for one Killing spinor. We show that there are three types of orbits of Spin(9,1) in the space of Weyl spinors which give rise to Killing spinors with stability subgroups…
We extend the refined G-structure classification of supersymmetric solutions of eleven dimensional supergravity. We derive necessary and sufficient conditions for the existence of an arbitrary number of Killing spinors whose common isotropy…
In the main part of this thesis, we present the foundations and initial results of the Spinorial Geometry formalism for solving Killing spinor equations. This method can be used for any supergravity theory, although we largely focus on D=11…
We present a Mathematica package for doing computations with gamma matrices, spinors, tensors and other objects, in any dimension and signature. The approach we use is based on defining the commutation relations of the relevant matrices,…
The introduction of (non-)geometric fluxes allows for N=1 moduli stabilisation in a De Sitter vacuum. The aim of this letter is to assess to what extent this is true in N=4 compactifications. First we identify the correct gauge algebra in…
This paper develops a geometric model for coupled two-state quantum systems (qubits), which is formulated using geometric (aka Clifford) algebra. It begins by showing how Euclidean spinors can be interpreted as entities in the geometric…
We summarize a unified and computationally efficient treatment of Fierz identities for form-valued pinor bilinears in various dimensions and signatures, using concepts and techniques borrowed from a certain approach to spinors known as…
For supersymmetric spacetimes in eleven dimensions admitting a null Killing spinor, a set of explicit necessary and sufficient conditions for the existence of any number of arbitrary additional Killing spinors is derived. The necessary and…
We describe how to calculate the amount of supersymmetry associated to a class of supergravity theories obtained by compactification on T-folds. We illustrate our discussion by calculating the degree of supersymmetry enjoyed by a particular…
We use geometric algebra techniques to give a synthetic and computationally efficient approach to Fierz identities in arbitrary dimensions and signatures, thus generalizing previous work. Our approach leads to a formulation which displays…
We solve the Killing spinor equations of supersymmetric IIB backgrounds which admit one supersymmetry and the Killing spinor has stability subgroup G_2 in Spin(9,1) x U(1). We find that such backgrounds admit a time-like Killing vector…
Motivated by the description of $\mathcal{N}=1$ M-theory compactifications to four-dimensions given by Exceptional Generalized Geometry, we propose a way to geometrize the M-theory fluxes by appropriately relating the compactification space…
We test the robustness of the conditions required for the existence of (supersymmetric) warped flux anti-de Sitter, de Sitter, and Minkowski backgrounds in supergravity theories using as examples suitable foliations of anti-de Sitter…
Superstring compactifications have been vigorously studied for over four decades, and have flourished involving an active iterative feedback between physics and (complex) algebraic geometry. This led to an unprecedented wealth of…
This note discusses the connection between generalised geometry and flux compactifications of string theory. Firstly, we explain in a pedestrian manner how the supersymmetry constraints of type II ${\mathcal{N}}=1$ flux compactifications…
We solve the Killing spinor equations of standard and massive IIA supergravities for a Killing spinor whose isotropy subgroup in Spin(9, 1) is SU(4) and identify the geometry of the spacetime. We demonstrate that the Killing spinor…