Related papers: B-type Landau-Ginzburg models with one-dimensional…
In this first of a series of three papers we outline an approach to classifying 4d $\mathcal{N}{=}2$ superconformal field theories at rank 2. The classification of allowed scale invariant $\mathcal{N}=2$ Coulomb branch geometries of…
Recent experimental evidence suggests the presence of an unconventional, nodal surface-su\-per\-con\-duc\-ting state in trigonal PtBi\textsubscript{2}. We construct a Ginzburg--Landau theory for the three superconducting order parameters,…
We evaluate the ideas of Pi-stability at the Landau-Ginzburg point in moduli space of compact Calabi-Yau manifolds, using matrix factorizations to B-model the topological D-brane category. The standard requirement of unitarity at the IR…
Given a 2-manifold, a fundamental question to ask is which groups can be realized as the isometry group of a Riemannan metric of constant curvature on the manifold. In this paper, we give a nearly complete classification of such groups for…
Let $n\geq 1$. The pro-unipotent completion of the pure braid group of $n$ points on a genus 1 surface has been shown to be isomorphic to an explicit pro-unipotent group with graded Lie algebra using two types of tools: (a) minimal models…
We consider the construction of a general tree level amplitude for the interactions between dynamical D-branes where the configurations have non-zero odd spin structure. Using Riemann Theta Identities we map the conditions for the…
We present new estimates on the two-dimensional Ginzburg-Landau energy of a type-II superconductor in an applied magnetic field varying between the second and third critical fields. In this regime, superconductivity is restricted to a thin…
Type IIA brane configurations are used to construct N=2 supersymmetric gauge theories in two dimensions. Using localization of chiral multiplets in ten-dimensional spacetime, supersymmetric non-linear sigma models with target space such as…
In this paper we prove the smoothness of the moduli space of Landau-Ginzburg models. We formulate and prove a Tian-Todorov theorem for the deformations of Landau-Ginzburg models, develop the necessary Hodge theory for varieties with…
We explore the phase structure of nonlinear sigma models with target spaces corresponding to compact quotients of hyperbolic space, focusing on the case of a hyperbolic genus-2 Riemann surface. The continuum theory of these models can be…
Based on the dispersionless KP (dKP) theory, we give a comprehensive study of the topological Landau-Ginzburg (LG) theory characterized by a rational potential. Writing the dKP hierarchy in a general form, we find that the hierarchy…
We study the wrapping of N type IIB Dp-branes on a compact Riemann surface $\Sigma$ in genus $g>1$ by means of the Sen-Witten construction, as a superposition of N' type IIB Dp'-brane/antibrane pairs, with $p'>p$. A background Neveu-Schwarz…
In this thesis we discuss some topics about topology and superstring backgrounds with D-branes. We start with a mathematical review about generalized homology and cohomology theories and the Atiyah-Hirzebruch spectral sequence, in order to…
We consider configurations of stacks of orientifold planes and D-branes wrapped on a non trivial internal space of the structure {(Gepner model)^{c=3n} x T^{2(3-n)}}/Z_N, for n=1,2,3. By performing simple moddings by discrete symmetries of…
In this paper, we classify completely hyperbolic 3-manifolds corresponding to geometric limits of Kleinian surface groups isomorphic to $\pi_1(S)$ for a finite-type hyperbolic surface $S$. In the first of the three main theorems, we…
We investigate a supersymmetric generalisation of topological recursion from two perspectives: algebraic and geometric. The algebraic side concerns a recursive structure encoded in modules of a super Virasoro algebra, and the geometric…
In this paper we construct topological sigma models which include a potential and are related to twisted massive supersymmetric sigma models. Contrary to a previous construction these models have no central charge and do not require the…
We describe a class of supersymmetric gauged linear sigma-model, whose target space is the infinite dimensional space of bundles on a Calabi-Yau 3- or 2-fold. This target space can be considered the configuration space of D-branes wrapped…
We construct Landau-Ginzburg models for numerically effective complete intersections in toric manifolds as partial compactifications of families of Laurent polynomials. We show a mirror statement saying that the quantum D-module of the…
In this work, we present two brane-world-type solutions in a two-dimensional (2D) dilaton gravity model with singular space-time backgrounds. By employing a first-order superpotential formalism, we first construct the 2D analogues of the…