Permutation branes and linear matrix factorisations

All the known rational boundary states for Gepner models can be regarded as permutation branes. On general grounds, one expects that topological branes in Gepner models can be encoded as matrix factorisations of the corresponding Landau-Ginzburg potentials. In this paper we identify the matrix factorisations associated to arbitrary B-type permutation branes.Comment: 43 pages. v2: References adde

Tensor Product and Permutation Branes on the Torus

We consider B-type D-branes in the Gepner model consisting of two minimal models at k=2. This Gepner model is mirror to a torus theory. We establish the dictionary identifying the B-type D-branes of the Gepner model with A-type Neumann and Dirichlet branes on the torus.Comment: 26 page

Sekolah Tinggi Pendidikan Syariat Islam di Kabupaten Bandung Barat

Islamic Higher Education aims to create ummat independency in applicating theology that based on Al-Qur\u27an and Hadist as the two main references. A perfect knowledge of theology is always connected to other knowledge, such as: Muamalah (trading), Fiqh (law), and Khilafah (governance system). This knowledge is gained directly and absolute from Allah SWT, not from other people in many opinions. Those are things concluded in theme “Islamic Architecture Based on Rasulullah SAW Sunnah”. Sunnah which are transformed into architecture with Islamic Higher education nuance of and education which is in accordance with theme and function of knowledge can be seen outside the building in forms of calligraphy, Islamic ornaments, mass creation reflecting Islam history, outer to inside transmssion (patterns), and knowledge element technologically applied into building function design. While room system following Rasul manner (Sunnah) is applied inside building

Correlation Between Gunung Padang and Sundanese Traditional Roof

Gunung Padang is the oldest prehistoric megaliths in Indonesia which has a function as a place of worship for the people who settled there about 2000BC according to its orientation and philosophy. Meanwhile after dark ages, people knowledge on building shelter arises therefore many traditional houses are build and had their philosophy implemented such as the vertical and horizontal beliefs in relation of human, nature, and divinity. This study concerns architecture identity correlation of place in the two eras because of cultural transition which can be observed until now. Gunung Padang has a similar vertical concept identity compare to Sundanese traditional roof according to both philosophy if the highest place is the most sacred place and describes the relationship between human, nature and divinity. The purpose of this study is to examine the correlation between Gunung Padang and the Sundanese traditional roof concept in religion and cultural aspect. Qualitative methods that leverages vernacular theory is used of the analysis methods

Opening Mirror Symmetry on the Quintic

Aided by mirror symmetry, we determine the number of holomorphic disks ending on the real Lagrangian in the quintic threefold. The tension of the domainwall between the two vacua on the brane, which is the generating function for the open Gromov-Witten invariants, satisfies a certain extension of the Picard-Fuchs differential equation governing periods of the mirror quintic. We verify consistency of the monodromies under analytic continuation of the superpotential over the entire moduli space. We reproduce the first few instanton numbers by a localization computation directly in the A-model, and check Ooguri-Vafa integrality. This is the first exact result on open string mirror symmetry for a compact Calabi-Yau manifold.Comment: 26 pages. v2: minor corrections and improvement

Moduli Webs and Superpotentials for Five-Branes

We investigate the one-parameter Calabi-Yau models and identify families of D5-branes which are associated to lines embedded in these manifolds. The moduli spaces are given by sets of Riemann curves, which form a web whose intersection points are described by permutation branes. We arrive at a geometric interpretation for bulk-boundary correlators as holomorphic differentials on the moduli space and use this to compute effective open-closed superpotentials to all orders in the open string couplings. The fixed points of D5-brane moduli under bulk deformations are determined.Comment: 41 pages, 1 figur

D-brane superpotentials and RG flows on the quintic

The behaviour of D2-branes on the quintic under complex structure deformations is analysed by combining Landau-Ginzburg techniques with methods from conformal field theory. It is shown that the boundary renormalisation group flow induced by the bulk deformations is realised as a gradient flow of the effective space time superpotential which is calculated explicitly to all orders in the boundary coupling constant.Comment: 24 pages, 1 figure, v2:Typo in (3.14) correcte

Defect Perturbations in Landau-Ginzburg Models

Perturbations of B-type defects in Landau-Ginzburg models are considered. In particular, the effect of perturbations of defects on their fusion is analyzed in the framework of matrix factorizations. As an application, it is discussed how fusion with perturbed defects induces perturbations on boundary conditions. It is shown that in some classes of models all boundary perturbations can be obtained in this way. Moreover, a universal class of perturbed defects is constructed, whose fusion under certain conditions obey braid relations. The functors obtained by fusing these defects with boundary conditions are twist functors as introduced in the work of Seidel and Thomas.Comment: 46 page

D-branes in Topological Minimal Models: the Landau-Ginzburg Approach

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 corresponding boundary OPE algebras as well as all disk correlators. We also construct examples of topological branes in E-type minimal models. We compare our results with the boundary state formalism, where possible, and find agreement.Comment: 29 pages, late