Related papers: Generalized structures of N=1 vacua

We describe the geometry of all type II common sector backgrounds with two supersymmetries. In particular, we determine the spacetime geometry of those supersymmetric backgrounds for which each copy of the Killing spinor equations admits a…

We consider flux vacua attractor equations in type IIA string theory compactified on generalized geometries with orientifold projections. The four-dimensional N=1 superpotential in this compactification can be written as the sum of the…

Generalised spin structures are necessary for placing fermions on manifolds that do not admit a standard spin structure. This is especially relevant in a dimensional reduction on such a manifold, which can then be compensated by using…

We study compactifications of Type IIB string theory on a K3 \times T^2/Z_2 orientifold in the presence of RR and NS flux. We find the most general supersymmetry preserving, Poincare invariant, vacua in this model. All the complex structure…

Let $f:N\rightarrow (M,g)$ be an oriented (or spin), complete, stable, minimal, immersed hypersurface. In this paper we establish various vanishing theorems for the space of $L^2$-harmonic forms and spinors (in the spin case) under suitable…

This talk adapts the available formalism to study a class of heterotic M-theory vacua with SO(10) grand unification group. Compactification to four dimensions with N = 1 supersymmetry is achieved on a torus fibered Calabi-Yau 3-fold Z = X /…

We define new Riemannian structures on 7-manifolds by a differential form of mixed degree which is the critical point of a (possibly constrained) variational problem over a fixed cohomology class. The unconstrained critical points…

Using the method of simple current extensions, asymmetric Gepner models of Type IIB with N=1 space-time supersymmetry are constructed. The combinatorics of the massless vector fields suggests that these classical Minkowski string vacua…

Vacuum compactifications may suffer from instabilities under small perturbations or tunnel effects; both are difficult to analyze. In this paper we consider the issue from a higher-dimensional perspective. We first look at how stability…

We show that various disconnected components of the moduli space of superstring vacua with 16 supercharges admit a rationale in terms of BPS un-orientifolds, i.e. type I toroidal compactifications with constant non-vanishing but quantized…

We study the possibility of achieving metastable de Sitter vacua in general N=2 to N=1 truncated supergravities without vector multiplets, and compare with the situations arising in N=2 theories with only hypermultiplets and N=1 theories…

We discuss supersymmetric $SU(2)$ gauge theory with a single matter field in the $I=3/2$ representation. This theory has a moduli space of exactly degenerate vacua. Classically it is the complex plane with an orbifold singularity at the…

We study the conditions under which a generic supergravity model involving chiral and vector multiplets can admit vacua with spontaneously broken supersymmetry and realistic cosmological constant. We find that the existence of such viable…

We derive a set of necessary and sufficient conditions for obtaining N=1 backgrounds of M-theory and type IIA strings in the presence of fluxes. Our metrics are warped products of four-dimensional Minkowski space-time with a curved internal…

We consider the SU(2)LxSU(2)R Standard Model brane embedding in an orientifold of T6/Z2xZ2. Within defined limits, we construct all such Standard Model brane embeddings and determine the relative number of flux vacua for each construction.…

This article is a write-up of the talk given in one of the mini-symposia of the 2024 European Congress of Mathematicians. I will explain some basics of the representation theory underlying Spin(10) and SU(5) Grand Unified Theories. I will…

After a short introduction to Matrix theory, we explain how can one generalize matrix models to describe toroidal compactifications of M-theory and the heterotic vacua with 16 supercharges. This allows us, for the first time in history, to…

We study the vacua of an $SU(3)\times SU(3)$-symmetric model with a bifundamental scalar. Structures of this type appear in various gauge theories such as the Renormalizable Coloron Model, which is an extension of QCD, or the Trinification…

We review the prospect of obtaining tree-level de Sitter (dS) vacua and slow-roll inflation models in string compactifications. Restricting ourselves to the closed string sector and assuming the absence of NSNS-sources, we classify the…

We consider examples of D=4 string theory vacua which, although globally non-geometric, admit a local description in terms of D=10 supergravity backgrounds. We analyze such backgrounds and find that the supersymmetry spinors vary…