We study geometric engineering of Argyres–Douglas superconformal theories realized by type IIB strings propagating in singular Calabi–Yau threefolds. We use this construction to count the degeneracy of light BPS states under small perturbations away from the conformal point, by computing the degeneracy of D3–branes wrapped around supersym-metric 3–cycles in the Calabi–Yau. We find finitely many...

We show how to construct supersymmetric three-generation models with gauge group and matter content of the Standard Model in the framework of non-simplyconnected elliptically fibered Calabi-Yau manifolds Z. The elliptic fibration on a cover Calabi-Yau, where the model has 6 generations of SU(5) and the bundle is given via the spectral cover description, has a second section leading to the neede...

Using mirror pairs (M3,W3) in type II superstring compactifications on Calabi-Yau threefols, we study, geometrically, F-theory duals of M-theory on seven manifolds with G2 holonomy. We first develop a new way for getting Landau Ginzburg (LG) CalabiYau threefols W3, embedded in four complex dimensional toric varieties, mirror to sigma model on toric Calabi-Yau threefolds M3. This method gives di...

Figure 1. A world of hidden, small dimensions. String theories are formulated in a world of 10 or 11 spacetime dimensions. According to those theories, a point in what appears to be four-dimensional spacetime is actually a tiny multidimensional space of its own. The purple blowup hints at the complexity of those minuscule spaces; it is a projection onto three dimensions of a 6D space called a C...

We construct general static black hole configuration for the theory of N = 2, d = 5 supergravity coupled to an arbitrary number of Abelian vector multiplets. The underlying very special geometry structure plays a major role in this construction. From the viewpoint of M-theory compactified on a Calabi-Yau threefold, these black holes are identified with BPS winding states of the membrane around ...

We construct general static black hole configuration for the theory of N = 2, d = 5 supergravity coupled to an arbitrary number of Abelian vector multiplets. The underlying very special geometry structure plays a major role in this construction. From the viewpoint of M-theory compactified on a Calabi-Yau threefold, these black holes are identified with BPS winding states of the membrane around ...

In this article, we prove that for a finite quiver Q the equivalence class of potential up to formal change variables complete path algebra $$\widehat{{{\mathbb {C}}}Q}$$ , is determined by its Jacobi together with in 0-th Hochschild homology represented assuming dimensional. This noncommutative analogue famous theorem Mather and Yau on isolated hypersurface singularities. We also right suffici...

THE SANDU FORMATION, consisting mainly of mudstone and marl, crops out sparsely in Guole Township, Jingxi County, southwestern Guangxi Province, China (Fig. 1). It yields a rich fauna of trilobite fossils, including species belonging to Shergoldia, Tamdaspis and Sinosaukia, which together indicate a late Furongian (latest Cambrian) age. These fossils are both abundant and well preserved. A larg...

Conformal algebra is an axiomatic description of the operator product expansion (or rather its Fourier transform) of chiral fields in a conformal field theory. It turned out to be an adequate tool for the realization of the program of the study of Lie (super)algebras and associative algebras (and their representations), satisfying the sole locality property [K3]. The first basic definitions and...

We study the half-BPS mesonic chiral ring of the N = 1 superconformal quiver theories arising from N D3-branes stacked at Y pq and Labc Calabi-Yau conical singularities. We map each gauge invariant operator represented on the quiver as an irreducible loop adjoint at some node, to an invariant monomial, modulo relations, in the gauged linear sigma model describing the corresponding bulk geometry...