Related papers: Algorithmic Algebraic Geometry and Flux Vacua
The design and implementation of parallel algorithms is a fundamental task in computer algebra. Combining the computer algebra system Singular and the workflow management system GPI-Space, we have developed an infrastructure for massively…
We summarise highlights from an ongoing research programme that aims, in the long run, at the ambitious goal of building a realistic, complete holographic composite-Higgs model. This contribution focuses on vacuum misalignment, by showing…
Non-geometric flux vacua have recently been revisited, leading to the remarkable discovery of isolated 4D ${\mathcal N}=1$ supersymmetric Minkowski vacua. These constructions rely on the non-renormalization of the superpotential, which is…
In this note we construct large ensembles of supersymmetry breaking solutions arising in the context of flux compactifications of type IIB string theory. This class of solutions was previously proposed in arXiv:hep-th/0402135 for which we…
In this talk I give an elementary introduction to the key algorithm used in recent applications of computational algebraic geometry to the subject of string phenomenology. I begin with a simple description of the algorithm itself and then…
We further develop on the study of the conditions for the existence of locally stable non-supersymmetric vacua with vanishing cosmological constant in supergravity models involving only chiral superfields. Starting from the two necessary…
We construct in this article a new realization of quantum geometry, which is obtained by quantizing the recently-introduced flux formulation of loop quantum gravity. In this framework, the vacuum is peaked on flat connections, and states…
Supergravity theories in more than four dimensions with grand unified gauge symmetries are an important intermediate step towards the ultraviolet completion of the Standard Model in string theory. Using toric geometry, we classify and…
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…
We obtain all homogeneous solutions of new massive gravity models on S^3 and AdS_3 by extending previously known results for the cosmological topologically massive theory of gravity in three dimensions. In all cases, apart from the…
We study the conditions an arbitrary flux configuration must fulfill in order to construct a 4d space-time of the type $AdS_2\times S^2$ from a type IIB supergravity flux compactification in which NS-NS fluxes are included. We present a…
We study conditions on general fluxes of massive Type IIA supergravity that lead to four-dimensional backgrounds with N = 1 supersymmetry. We derive these conditions in the case of SU(3)- as well as SU(2)-structures. SU(3)-structures imply…
We demonstrate that flux compactifications of type IIA string theory can classically stabilize all geometric moduli. For a particular orientifold background, we explicitly construct an infinite family of supersymmetric vacua with all moduli…
Computations in Dynamical Triangulation Models of Four-Dimensional Quantum Gravity involve weighted averaging over sets of all distinct triangulations of compact four-dimensional manifolds. In order to be able to perform such computations…
Many problems in computational geometry are not stated in graph-theoretic terms, but can be solved efficiently by constructing an auxiliary graph and performing a graph-theoretic algorithm on it. Often, the efficiency of the algorithm…
The virial expansion provides a non-perturbative view into the thermodynamics of quantum many-body systems in dilute regimes. While powerful, the expansion is challenging as calculating its coefficients at each order $n$ requires analyzing…
We perform a systematic analysis of generic string flux compactifications, making use of Exceptional Generalized Geometry (EGG) as an organizing principle. In particular, we establish the precise map between fluxes, gaugings of maximal 4d…
We continue the investigation into non-maximally symmetric compactifications of the heterotic string. In particular, we consider compactifications where the internal space is allowed to depend on two or more external directions. For…
Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical…
Finding vacua for the four dimensional effective theories for supergravity which descend from flux compactifications and analyzing them according to their stability is one of the central problems in string phenomenology. Except for some…