Related papers: Holomorphic Gauge Fields on $B$-Branes
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…
Considering the $B$-branes over the complex projective space ${\mathbb P}^n$ as the objects of the bounded derived category $D^b({\mathbb P}^n)$, we prove that the cardinal of the set of holomorphic gauge fields on a given $B$-brane…
Considering the $B$-branes over a complex manifold $Y$ as objects of the bounded derived category $D^b(Y)$, we define holomorphic gauge fields on $B$-branes and the Yang-Mills functional for these fields.These definitions are a…
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 $\mathrm{Spin}^c$…
The geometric phase that appears in the effects of Aharonov-Bohm type is interpreted in the frame of Deligne's version of the Riemann-Hilbert correspondence. We extend also the concept of flat gauge field to $B$-branes which are coherent…
We consider homological mirror symmetry in the context of hypertoric varieties, showing that appropriate categories of B-branes (that is, coherent sheaves) on an additive hypertoric variety match a category of A-branes on a Dolbeault…
We show that the description of the holomorphic $\mathbb C \mathrm P^1$-bundle associated to a holomorphic projective structure on a Riemann surface in terms of the principal bundle of projective $2$-frames extends very well to the setting…
We present the first example of a Kahler potential for heterotic M-theory which includes gauge bundle moduli. These moduli describe the background gauge field configurations living on the orbifold fixed planes. We concentrate on the bundle…
We define a particular class of topological field theories associated to open strings and prove the resulting D-branes and open strings form the bounded derived category of coherent sheaves. This derivation is a variant of some ideas…
Given a flat gauge field $\nabla$ on a vector bundle $F$ over a manifold $M$ we deduce a necessary and sufficient condition for the field $\nabla+ E$, with $E$ an ${\rm End}(F)$-valued $1$-form, to be a Yang-Mills field. For each curve of…
We propose a conjecture on the structure of the bounded derived category of coherent sheaves of the moduli space rank $2$ parabolic bundles on $\mathbb{P}^1$.
We notice that, for branes wrapped on complex analytic subvarieties, the algebraic-geometric version of K-theory makes the identification between brane-antibrane pairs and lower-dimensional branes automatic. This is because coherent sheaves…
In this paper we prove first a general theorem on semiorthogonal decompositions in derived categories of coherent sheaves for flat families over a smooth base. Based on the results of math.AG/0510670, we then show that the derived…
In this note we identify two complex structures (one is given by algebraic geometry, the other by gauge theory) on the set of isomorphism classes of holomorphic bundles with section on a given compact complex manifold. In the case of line…
This elementary survey article was prepared for a talk at the 2016 Superschool on Derived Categories and D-branes. The goal is to outline an identification of the bounded derived category of coherent sheaves on a Calabi-Yau threefold with…
Graded vector bundles over a given $\mathbb{Z}$-graded manifold can be defined in three different ways: certain sheaves of graded modules over the structure sheaf of the base graded manifold, finitely generated projective graded modules…
Given a smooth complex projective variety $M$ and a smooth closed curve $X \subset M$ such that the homomorphism of fundamental groups $\pi_1(X) \rightarrow \pi_1(M)$ is surjective, we study the restriction map of Higgs bundles, namely from…
Given a compact hyperkaehler manifold $M$ and a holomorphic bundle B over $M$, we consider a Hermitian connection $\nabla$ on B which is compatible with all complex structures on $M$ induced by the hyperkaehler structure. Such a connection…
It has recently been observed that, in contrast to the classical case, holomorphic structures on line bundles over the quantum projective line are not uniquely determined by degree. We formulate a fixed-point-theoretic framework for the…
For each holomorphic vector bundle we construct a holomorphic bundle 2-gerbe that geometrically represents its second Beilinson-Chern class. Applied to the cotangent bundle, this may be regarded as a higher analogue of the canonical line…