相关论文: On G/H geometry and its use in M-theory compactifi…

Supersymmetric grand unified models based on SO(10) gauge symmetry have many desireable features, including the unification of Yukawa couplings. Using D-term contributions to scalar masses arising from the breakdown of SO(10), Yukawa…

The comparison theory for the Riccati equation satisfied by the shape operator of parallel hypersurfaces is generalized to semi-Riemannian manifolds of arbitrary index, using one-sided bounds on the Riemann tensor which in the Riemannian…

This paper advocates a novel framework for segmenting a dataset in a Riemannian manifold $M$ into clusters lying around low-dimensional submanifolds of $M$. Important examples of $M$, for which the proposed clustering algorithm is…

We study W-algebras obtained by quantum Hamiltonian reduction of $sl(Mn)$ associated to the $sl(2)$ embedding of rectangular type. The algebra can be realized as the asymptotic symmetry of higher spin gravity with $M \times M$ matrix valued…

We define the notion of a Killing (super)algebra for a connection on a spinor bundle associated to a generalised spin structure on a pseudo-Riemannian manifold of any signature. We are led naturally to include in the even subspace not only…

We provide some examples of Killing superalgebras on 2-dimensional pseudo-Riemannian manifolds within the theoretical framework established in [SIGMA 21 (2025), 081, 61 pages, arXiv:2409.11306]. We compute the Spencer cohomology group…

In this thesis I review various aspects of the AdS_4/CFT_3 correspondence, where AdS_4 supergravity arises from compactification of M-theory on a coset space G/H and preserves N<8 supersymmetries. One focal point of my review is that the…

We consider compactifications of type IIA superstring theory on mirror-folds obtained as K3 fibrations over two-tori with non-geometric monodromies involving mirror symmetries. At special points in the moduli space these are asymmetric…

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 reconsider the Kaluza Klein compactifications of D=11 supergravity on AdS_4x(G/H)_7 manifolds that were classified in the eighties, in the modern perspective of AdS_4/CFT_3 correspondence. We focus on one of the three N=2 cases:…

It is often argued that in the class of non-supersymmetric SO(10) grand unified theories there is barely any room for reconciling the lower bound on the position of the GUT scale emerging from the proton decay searches and the lower limit…

We systematically study calibrated geometry in hyperk\"ahler cones $C^{4n+4}$, their 3-Sasakian links $M^{4n+3}$, and the corresponding twistor spaces $Z^{4n+2}$, emphasizing the relationships between submanifold geometries in various…

We reduce the classification of all supersymmetric backgrounds in eleven dimensions to the evaluation of the supercovariant derivative and of an integrability condition, which contains the field equations, on six types of spinors. We…

We study the breaking of a supersymmetric SO(10) GUT in 6 dimensions by orbifold compactification. In 4 dimensions we obtain a N=1 supersymmetric theory with the standard model gauge group enlarged by an additional U(1) symmetry. The…

We present SU$(2|1)$ supersymmetric mechanics on $n$-dimensional Riemannian manifolds within the Hamiltonian approach. The structure functions including prepotentials entering the supercharges and the Hamiltonian obey extended curved WDVV…

We classify the supersymmetric solutions of minimal $N=2$ gauged supergravity in four dimensions with neutral signature. They are distinguished according to the sign of the cosmological constant and whether the vector field constructed as a…

We consider three-dimensional ${\mathcal N}=2$ supersymmetric field theories defined on general complex-valued backgrounds of Euclidean new minimal supergravity admitting two Killing spinors of opposite $R$-charges. We compute partition…

We present a theorem describing a dual relation between the local geometry of a space admitting a symmetric second-rank Killing tensor, and the local geometry of a space with a metric specified by this Killing tensor. The relation can be…

Negatively-curved, maximally symmetric hyperbolic spaces enjoy a number of remarkable properties that can be traced back to Riemannian geometry, group theory and algebraic geometry. In this note we recall some such properties and find $H_n$…

Consider a sequence of closed, orientable surfaces of fixed genus $g$ in a Riemannian manifold $M$ with uniform upper bounds on mean curvature and area. We show that on passing to a subsequence and choosing appropriate parametrisations, the…