Related papers: The gap phenomenon in parabolic geometries
The supersymmetric generalization of dilatations in the presence of the dilaton is defined. This is done by defining the supersymmetric dilaton geometry which is motivated by the supersymmetric volume preserving diffeomorphisms. The…
To certain types of generic distributions (subbundles in a tangent bundle) one can associate canonical Cartan connections. Many of these constructions fall into the class of parabolic geometries. The aim of this article is to show how…
The mapping class group $\Gamma$ of the complement of a Cantor set in the plane arises naturally in dynamics. We show that the ray graph, which is the analog of the complex of curves for this surface of infinite type, has infinite diameter…
Using Wederburn's main theorem and a result of Gerstenhaber we prove that, over a field of characteristic zero, the maximal dimension of a proper unital subalgebra in the $n \times n$ matrix algebra is $n^2 - n + 1$ and furthermore this…
We discuss our attempts to generalize the known examples of dualities in N=1 supersymmetric gauge theories to exceptional gauge groups. We derive some dual pairs from known examples connected to exceptional groups and find an interesting…
We argue that extra dimensions with a properly chosen compactification scheme could be a natural source for emergent gauge symmetries. Actually, some proposed vector field potential terms or polynomial vector field constraints introduced in…
We show that in the context of two-dimensional sigma models minimal coupling of an ordinary rigid symmetry Lie algebra $\mathfrak{g}$ leads naturally to the appearance of the "generalized tangent bundle" $\mathbb{T}M \equiv TM \oplus T^*M$…
We establish the submaximal symmetry dimension for Riemannian and Lorentzian conformal structures. The proof is based on enumerating all subalgebras of orthogonal Lie algebras of sufficiently large dimension and verifying if they stabilize…
Spontaneous symmetry breaking is a cornerstone of modern physics, defining a wealth of phenomena in condensed-matter and high-energy physics, and beyond. It requires an infinite number of degrees of freedom, and even then, for continuous…
Conserved quantities are obtained and analyzed in the new models with global scale invariance recently proposed. Such models allow for non tivial scalar field potentials and masses for particles, so that the scale symmetry must be broken…
We show that the natural presence of flat directions in supersymmetric theories allows for nonrestoration of global and/or gauge symmetries. This has important cosmological consequences for supersymmetric GUTs and in particular it offers a…
We construct a series of examples of non--flat non--homogeneous parabolic geometries that carry a symmetry of the parabolic geometry at each point.
We consider gauge theories defined in higher dimensions where the extra dimensions form a fuzzy space (a finite matrix manifold). We reinterpret these gauge theories as four-dimensional theories with Kaluza-Klein modes. We then perform a…
We locate gaps in the spectrum of a Hamiltonian on a periodic cuboidal (and generally hyperrectangular) lattice graph with $\delta$ couplings in the vertices. We formulate sufficient conditions under which the number of gaps is finite. As…
Maximal parabolic subalgebras of untwisted affine Kac-Moody algebras were studied in the context of Borel-de Siebenthal theory in [13], where they were realized as certain equivariant map algebras with a non-free abelian group action. In…
It is well known that the toroidal dimensional reduction of supergravities gives rise in three dimensions to theories whose bosonic sectors are described purely in terms of scalar degrees of freedom, which parameterise sigma-model coset…
We have analyzed the breakdown of global supersymmetry by a non-vanishing expectation value of the fifth component of the graviphoton on warped S^1/Z_2 orbifolds. It has been demonstrated that the setups where such a breakdown is possible…
We develop an algebraic version of Cartan method of equivalence or an analog of Tanaka prolongation for the (extrinsic) geometry of curves of flags of a vector space $W$ with respect to the action of a subgroup $G$ of the $GL(W)$. Under…
We propose a higher dimensional scenario to solve the gauge hierarchy problem. In our formulation, a crucial observation is that a supersymmetric structure is hidden in the 4d spectrum of any gauge invariant theories with compact extra…
We study various aspects of spontaneous symmetry breaking in theories that possess higher-form symmetries, which are symmetries whose charged objects have a dimension $p>0$. We first sketch a proof of a higher version of Goldstone's…