Related papers: Non-split superstrings of dimension $(1|2)$

We propose a supersymmetric SU(5) orbifold GUT in 5 dimensions in which supersymmetry breaking at the boundaries give rise to split supersymmetry spectrum. The extra dimension is compactified on a $S^1/Z_2 \times Z_2^\prime$ orbifold having…

Let $X$ be a submanifold of dimension $d\geq 2$ of the complex projective space $\mathbb P^n$. We prove results of the following type. i) If $X$ is irregular and $n=2d$ then the normal bundle $N_{X|\mathbb P^n}$ is indecomposable. ii) If…

We present a scenario wherein the anomalous U(1) D-term of string origin triggers supersymmetry breaking and generates naturally a Split Supersymmetry spectrum. When the gaugino and the Higgsino masses (which are of the same order of…

We study in detail the underlying graded geometric structure of abelian N=2 supersymmetric Chern-Simons theory in $(2+1)$-dimensions. This structure is an attribute of the hidden unbroken one dimensional N=2 supersymmetries that the system…

We provide the first holographic evidence for the existence of a non-supersymmetric conformal manifold arising from exactly marginal but supersymmetry-breaking deformations of a superconformal three-dimensional field theory. In particular,…

For every non-vanishing spinor field on a Riemannian spin seven-manifold, Crowley, Goette, and Nordstr\"om defined the so-called $\nu$-invariant. This is an integer modulo $48$ that detects connected components of the moduli space of…

In this thesis we investigate a new formalism for supergeometry which focuses on the categorical properties of the theory. This approach is our main tool in the subsequent investigation of a global analytic approach to the construction of…

A graph is a split graph if its vertex set can be partitioned into a clique and a stable set. A split graph is unbalanced if there exist two such partitions that are distinct. Cheng, Collins and Trenk (2016), discovered the following…

We prove an analogue of the Madsen-Weiss theorem for high dimensional manifolds. For example, we explicitly describe the ring of characteristic classes of smooth fibre bundles whose fibres are connected sums of g copies of S^n x S^n, in the…

A partition into distinct parts is refinable if one of its parts $a$ can be replaced by two different integers which do not belong to the partition and whose sum is $a$, and it is unrefinable otherwise. Clearly, the condition of being…

In this paper, we prove several rigidity results for complete noncompact manifolds with nonnegative intermediate curvatures. We show that when either $3\leq n\leq 5$, $1\leq m\leq n-1$, or $6\leq n\leq 7$, $m\in \{1,n-1,n-2\}$, any manifold…

The perturbative analysis of models of open and closed superstrings presents a number of surprises. For instance, variable numbers of antisymmetric tensors ensure their consistency via generalized Green-Schwarz cancellations and a novel…

In the present paper we prove that the Hilbert scheme of 0-dimensional subspaces on supercurves of dimension $(1|1)$ exists and it is smooth. We show that the Hilbert scheme is not split in general.

Stacks have become a prevalent tool in studying problems with connections to String Theory, hence we see a need to develop a theory of supersymmetric stacks proper. We first define derived stacks on $\mathbb{Z}_2$-bi-graded k-modules…

In this paper, we disprove the long-standing conjecture that any complete geometric graph on $2n$ vertices can be partitioned into $n$ plane spanning trees. Our construction is based on so-called bumpy wheel sets. We fully characterize…

The question of which manifolds are spin or spin^c has a simple and complete answer. In this paper we address the same question for spin^h manifolds, which are less studied but have appeared in geometry and physics in recent decades. We…

We extend the spectral generalization of the Cheeger-Gromoll splitting theorem to smooth metric measure space. We show that if a complete non-compact weighted Riemannian manifold $(M,g,e^{-f}\,dvolg)$ of dimension $n\ge 2$ has at least two…

A. Reid showed that if $\Gamma_1$ and $\Gamma_2$ are arithmetic lattices in $G = \operatorname{PGL}_2(\mathbb R)$ or in $\operatorname{PGL}_2(\mathbb C)$ which give rise to isospectral manifolds, then $\Gamma_1$ and $\Gamma_2$ are…

There exist myriads of off-shell worldline supermultiplets for (N{\leq}32)-extended supersymmetry in which every supercharge maps a component field to precisely one other component field or its derivative. A subset of these extends to…

In 1987, Kalai proved that stacked spheres of dimension $d\geq 3$ are characterised by the fact that they attain equality in Barnette's celebrated Lower Bound Theorem. This result does not extend to dimension $d=2$. In this article, we give…