Related papers: B-type Landau-Ginzburg models with one-dimensional…
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 short note we apply methods of Aspinwall-Katz to compute superpotentials of D-branes wrapped on more general obstructed rational curves in Calabi-Yau threefolds. We find an a priori unexpected match between superpotentials from…
The mirror dual of a smooth toric Fano surface $X$ equipped with an anticanonical divisor $E$ is a Landau-Ginzburg model with superpotential, W. Carl-Pumperla-Siebert give a definition of the the superpotential in terms of tropical disks…
We investigate the super Landau-Ginzburg mirrors of gauged linear sigma models which, in an appropriate low energy limit, reduce to nonlinear sigma models with Kaehler supermanifold target spaces of nonnegative super-first Chern class.
In arXiv:1711.05958, arXiv:2103.12673, the authors derive one-dimensional Landau-Ginzburg mirrors of Dubrovin-Zhang Frobenius manifolds constructed on regular orbit spaces of an extension of affine Weyl groups. We generalise the method…
We prove that every orientable infinite type surface without boundary and finite genus has a Riemann surface structure such that its modular group of quasiconformal homeomorphisms is countable.
We study geodesics on a planar Riemann surface of infinite type having a single infinite end. Of particular interest is the class of geodesics that go out the infinite end in a most efficient manner. We investigate properties of these…
We review various aspects of the topological classification of D-brane charges in K-theory, focusing on techniques from geometric K-homology and Kasparov's KK-theory. The latter formulation enables an elaborate description of D-brane charge…
We study deformations of Landau-Ginzburg D-branes corresponding to obstructed rational curves on Calabi-Yau threefolds. We determine D-brane moduli spaces and D-brane superpotentials by evaluating higher products up to homotopy in the…
B-type D-branes can be obtained from matrix factorizations of the Landau-Ginzburg superpotential. We here review this promising approach to learning about the spacetime superpotential of Calabi-Yau compactifications. We discuss the grading…
We consider Landau-Ginzburg models with possibly different superpotentials glued together along one-dimensional defect lines. Defects preserving B-type supersymmetry can be represented by matrix factorisations of the difference of the…
We study marginal deformations of B-type D-branes in Landau-Ginzburg orbifolds. The general setup of matrix factorizations allows for exact computations of F-term equations in the low-energy effective theory which are much simpler than in a…
The purpose of this paper is threefold: First of all the topological aspects of the Landau Hamiltonian are reviewed in the light (and with the jargon) of theory of topological insulators. In particular it is shown that the Landau…
We will show that any open Riemann surface $M$ of finite genus is biholomorphic to an open set of a compact Riemann surface. Moreover, we will introduce a quotient space of forms in $M$ that determines if $M$ has finite genus and also the…
We study the Ginzburg-Landau equations on Riemann surfaces of arbitrary genus. In particular: - we construct explicitly the (local moduli space of gauge-equivalent) solutions in a neighbourhood of the constant curvature ones; - classify…
We construct a topological Landau-Ginzburg formulation of the two-dimensional string at the self-dual radius. The model is an analytic continuation of the $A_{k+1}$ minimal model to $k=-3$. We compute the superpotential and calculate…
This paper concerns constructing topological sigma models governing maps from semirigid super Riemann surfaces to general target supermanifolds. We define both the A model and B model in this general setup by defining suitable BRST…
We generalize the worldsheet derivation of the topological open/closed string duality given in hep-th/0205297 to cases when there are different types of D branes on the open string side. We use the mirror Landau-Ginzburg description to…
We study conformal defects in two important examples of string theory orbifolds. First, we show that topological defects in the language of Landau-Ginzburg models carry information about the RG flow between the non-compact orbifolds…
We argue that D-branes corresponding to rational B boundary states in a Gepner model can be understood as fractional branes in the Landau-Ginzburg orbifold phase of the linear sigma model description. Combining this idea with the…