Related papers: Branes on $G$-manifolds

By a $B$-regular variety, we mean a smooth projective variety over $C$ admitting an algebraic action of the upper triangular Borel subgroup $B \subset SL_2(C)$ such that the unipotent radical in $B$ has a unique fixed point. A result of M.…

This work is concerned with branes and differential equations for one-parameter Calabi-Yau hypersurfaces in weighted projective spaces. For a certain class of B-branes we derive the inhomogeneous Picard--Fuchs equations satisfied by the…

Novel theories appear on the world-volume of branes by orienting B fields along various directions of the branes. We review some of the earlier developments and explore many new examples of these theories. In particular, among other things,…

We initiate the study of Brane Gas Cosmology (BGC) on manifolds with non-trivial holonomy. Such compactifications are required within the context of superstring theory in order to make connections with realistic particle physics. We study…

We define the category of B-branes in a (not necessarily affine) Landau-Ginzburg B-model, incorporating the notion of R-charge. Our definition is a direct generalization of the category of perfect complexes. We then consider pairs of…

In this thesis the close relationship between the topological $K$-homology group of the spacetime manifold $X$ of string theory and D-branes in string theory is examined. An element of the $K$-homology group is given by an equivalence class…

We define and discuss G-formality for certain spaces endowed with an action by a compact Lie group. This concept is essentially formality of the Borel construction of the space in a category of commutative differential graded algebras over…

We review some recent results on D-branes on Calabi-Yau (CY) manifolds. We show the existence of structures (helices and quivers) which enable one to make statements about large families of D-branes in various phases of the Gauged Linear…

By a direct CFT computation, the spectrum of the topological B-model is compared to Ext groups of sheaves. A match can only be made if abstract vector bundles on holomorphic submanifolds are twisted by the canonical $\mathrm{Spin}^c$…

We investigate the formal deformation theory of (rank 1) branes on generalized complex (GC) manifolds. This generalizes, for example, the deformation theory of a complex submanifold in a fixed complex manifold. For each GC brane…

For a compact group G, we give a sufficient condition for embedding one G-equivariant vector bundle into another one and for a stable isomorphism between two such bundles to imply an isomorphism. Our criteria involve multiplicities of…

We present a new categorical classification framework for D-brane charges on noncommutative manifolds using methods of bivariant K-theory. We describe several applications including an explicit formula for D-brane charge in cyclic homology,…

We present an overview of the ways in which D-brane charges are classified in terms of K-theory, emphasizing the natural physical interpretations of a homological classification within a topological setting.

Let $\Gamma$ be a finite group acting on a Lie group $G$. We consider a class of group extensions $1 \to G \to \hat{G} \to \Gamma \to 1$ defined by this action and a $2$-cocycle of $\Gamma$ with values in the centre of $G$. We establish and…

We study D-branes on Calabi-Yau manifolds, carrying charges which are torsion elements of the K-theory. Interesting physics ensues when we follow these branes into nongeometrical phases of the compactification. On the level of K-theory, we…

We investigate D-branes on a noncompact singular Calabi-Yau manifold by using the boundary CFT description, and calculate the open string Witten indices between the boundary states. The B-type D-branes turn out to be characterized by the…

Theories of gravity coupled to forms and dilatons may admit as solutions zero binding energy configurations of intersecting closed extremal branes. In such configurations, some branes may open on host closed branes. Properties of extremal…

Let $(X,T^{1,0}X)$ be a $(2n+1+d)$-dimensional compact CR manifold with codimension $d+1$, $d\geq1$, and let $G$ be a $d$-dimensional compact Lie group with CR action on $X$ and $T$ be a globally defined vector field on $X$ such that…

We explicitly construct a solution of eight-dimensional gauged supergravity representing D6-branes wrapped on six-cycles inside Calabi-Yau fourfolds. The solution preserves two supercharges and asymptotically is a cone with the coset space…

Considering $B$-branes over a complex manifold $X$ as objects of the bounded derived category of coherent sheaves over $X$, we define holomorphic gauge fields on $B$-branes and introduce the Yang-Mills functional for these fields. These…