Related papers: Landau-Ginzburg Models, D-branes, and Mirror Symme…
This paper is an introduction to Homological Mirror Symmetry, derived categories, and topological D-branes aimed mainly at a mathematical audience. In the paper we explain the physicists' viewpoint of the Mirror Phenomenon, its relation to…
This is an exposition of recent progress in the categorical approach to D-brane physics. I discuss the physical underpinnings of the appearance of homotopy categories and triangulated categories of D-branes from a string field theoretic…
We study D-branes extended in T^2/Z_4 using the mirror description as a tensor product of minimal models. We describe branes in the mirror both as boundary states in minimal models and as matrix factorizations in the corresponding…
Recently, mirror symmetry is derived as T-duality applied to gauge systems that flow to non-linear sigma models. We present some of its applications to study quantum geometry involving D-branes. In particular, we show that one can employ…
We study the Landau-Ginzburg (LG) mirror theory of the non-linear sigma model on the ALE space ${\cal M}$ obtained by resolving the singularity of the orbifold ${\bf C}^2/{\bf Z}_N$. In the LG description, the data of the BPS spectrum and…
In spite of physics terms in the title, this paper is purely mathematical. Its purpose is to introduce triangulated categories related to singularities of algebraic varieties and establish a connection of these categories with D-branes in…
These are expository notes based on a talk given at the Superschool on derived categories and D-branes at University of Alberta in July of 2016. The goal of these notes is to give a motivated introduction to the Strominger-Yau-Zaslow (SYZ)…
We survey on the recent progress toward mirror symmetry between Landau-Ginzburg models.
This is a short nontechnical note summarizing the motivation and results of my recent work on D-brane categories. I also give a brief outline of how this framework can be applied to study the dynamics of topological D-branes and why this…
This is a write-up of lectures given at the 1998 Spring School at the Abdus Salam ICTP. We give a conceptual introduction to D-geometry, the study of geometry as seen by D-branes in string theory, and to noncommutative geometry as it has…
We review in elementary, non-technical terms the description of topological B-type of D-branes in terms of boundary Landau-Ginzburg theory, as well as some applications.
We study topological D-branes of type B in N=2 Landau-Ginzburg models, focusing on the case where all vacua have a mass gap. In general, tree-level topological string theory in the presence of topological D-branes is described…
We revisit open string mirror symmetry for the elliptic curve, using matrix factorizations for describing D-branes on the B-model side. We show how flat coordinates can be intrinsically defined in the Landau-Ginzburg model, and derive the…
We study D-branes in topologically twisted N=2 minimal models using the Landau-Ginzburg realization. In the cases of A and D-type minimal models we provide what we believe is an exhaustive list of topological branes and compute the…
A T6 orbifold compactification is discussed from the somewhat unconventional perspective as the large radius limit of a Landau-Ginzburg model. The features of the model are in principle familiar, but the way they enter here is different…
We describe supersymmetric A-branes and B-branes in open N=(2,2) dynamically gauged nonlinear sigma models (GNLSM), placing emphasis on toric manifold target spaces. For a subset of toric manifolds, these equivariant branes have a mirror…
We study D-branes in Kazama-Suzuki models by means of the boundary state description. We can identify the boundary states of Kazama-Suzuki models with the solitons in N=2 Landau-Ginzburg theories. We also propose a geometrical…
We finalize the study of collapsing D-branes in one-parameter models by completing the analysis of the associated hypergeometric hierarchy. This brings further evidence that the phenomenon of collapsing 6-branes at the mirror of the…
We study (2,2) supersymmetric field theories on two-dimensional worldsheet with boundaries. We determine D-branes (boundary conditions and boundary interactions) that preserve half of the bulk supercharges in non-linear sigma models, gauged…
This thesis is concerned with D-branes in topological string theory, focusing on the description of B-type D-branes in topological Landau-Ginzburg models. Such D-branes are characterized by matrix factorizations of the Landau-Ginzburg…