Related papers: The gap phenomenon in parabolic geometries

We consider models with a noncompact symmetry in the framework of $\mathcal{N}=1$ supersymmetry. Contrary to the conventional approach, the noncompact symmetry is realized linearly on all fields without constraints. The models are…

For every parabolic subgroup $P$ of a Lie supergroup $G$ the homogeneous superspace $G/P$ carries a $G$-invariant supergeometry. We address the quesiton whether $\mathfrak{g}=\operatorname{Lie}(G)$ is the maximal symmetry of this…

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…

This paper considers asymptotically hyperbolic manifolds with a finite boundary intersecting the usual infinite boundary -- cornered asymptotically hyperbolic manifolds -- and proves a theorem of Cartan-Hadamard type near infinity for the…

For Cartan geometries admitting automorphisms with isotropies satisfying a particular, loosely dynamical property on their model geometries, we demonstrate the existence of an open subset of the geometry with trivial holonomy. This…

In this paper, we introduce the comaximal graph $\Gamma(L)$ of a finite-dimensional Lie algebra $L$, whose vertices are the nontrivial proper Lie subalgebras of $L$ over a field $\mathbb{F}$, and two vertices $A$ and $B$ are adjacent if and…

A simplified Randall-Sundrum-like model in 6 dimensions is discussed. The extra two dimensions correspond to the cone. The effective four-dimensional scalar self-interacting theory is studied at one-loop level. The contributions due to…

We show that in a general hidden sector model, supersymmetry breaking necessarily generates at one-loop a scalar and gaugino mass as a consequence of the super-Weyl anomaly. We study a scenario in which this contribution dominates. We…

Grand unification of gauge couplings and fermionic representations remains an appealing proposal to explain the seemingly coincidental structure of the Standard Model. However, to realise the Standard Model at low energies, the unified…

Let $\mathcal{M}=\Gamma\backslash\mathbb{H}^{d+1}$ be a geometrically finite hyperbolic manifold with critical exponent exceeding $d/2$. We obtain a precise asymptotic expansion of the matrix coefficients for the geodesic flow in…

Using the theory of Weyl structures, we give a natural generalization of the notion of essential conformal structures and conformal Killing fields to arbitrary parabolic geometries. We show that a parabolic structure is inessential whenever…

Using gauge theory, we describe how to construct generalized Kahler geometries with (2,2) two-dimensional supersymmetry, which are analogues of familiar examples like projective spaces and Calabi-Yau manifolds. For special cases, T-dual…

C-projective structures are analogues of projective structures in the complex setting. The maximal dimension of the Lie algebra of c-projective symmetries of a complex connection on an almost complex manifold of C-dimension $n>1$ is…

These notes are devoted to the problem of finite-dimensional reduction for parabolic PDEs. We give a detailed exposition of the classical theory of inertial manifolds as well as various attempts to generalize it based on the so-called…

In a completely systematic and geometric way, we derive maximal and half-maximal supersymmetric gauged double field theories in lower than ten dimensions. To this end, we apply a simple twisting ansatz to the $D=10$ ungauged maximal and…

An intrinsic definition in terms of conformal capacity is proposed for the conformal type of a Carnot--Carath\'eodory space (parabolic or hyperbolic). Geometric criteria of conformal type are presented. They are closely related to the…

A mechanism of supersymmetry breaking in two or four-dimensions is given, in which the breaking is related to the Fermat's last theorem. It is shown that supersymmetry is exact at some irrational number points in parameter space, while it…

We show that a quantum-mechanical N=2 supersymmetry is hidden in 4d mass spectrum of any gauge invariant theories with extra dimensions. The N=2 supercharges are explicitly constructed in terms of differential forms. The analysis can be…

This note is about the geometry of the pants graph P(S), a natural simplicial graph associated to a finite type topological surface S where vertices represents pants decompositions. The main result in this note ascserts that for a…

We develop the theory of integrable representations for an arbitrary maximal parabolic subalgebra of an affine Lie algebra. We see that such subalgebras can be thought of as arising in a natural way from a Borel--de Siebenthal pair of…