Related papers: A Tropical Look at Coisotropic Branes and Quantiza…
We study tropical line arrangements associated to a three-regular graph $G$ that we refer to as \emph{tropical graph curves}. Roughly speaking, the tropical graph curve associated to $G$, whose genus is $g$, is an arrangement of $2g-2$…
We construct a general framework for tropical differential equations based on idempotent semirings and an idempotent version of differential algebra. Over a differential ring equipped with a non-archimedean norm enhanced with additional…
This work deals with the presence of thick branes in a model with two source scalar fields that interact with one another in a very specific way. The model is new, capable of generating kinklike configurations that engender important…
We consider D3 branes at orbifolded conifold singularities which are not quotient singularities. We use toric geometry and gauged linear sigma model to study the moduli space of the gauge theories on the D3 branes. We find that…
Tropical mathematics redefines the rules of arithmetic by replacing addition with taking a maximum, and by replacing multiplication with addition. After briefly discussing a tropical version of linear algebra, we study polynomials build…
We use toric geometry to investigate the recently proposed relation between a set of D3 branes at a generalized conifold singularity and type IIA configurations of D4 branes stretched between a number of relatively rotated NS5 branes. In…
We define transversal tropical triangles (affine and projective) and characterize them via six inequalities to be satisfied by the coordinates of the vertices. We prove that the vertices of a transversal tropical triangle are tropically…
We present a systematic analysis of possible bound states of M-brane solutions (including waves and monopoles) by using the solution generating technique of reduction of M-brane to 10 dimensions, use of T-duality and then lifting back to 11…
We introduce T-duality invariant versions of D-branes in doubled geometry using a global covariant framework based on para-Hermitian geometry and metric algebroids. We define D-branes as conformal boundary conditions for the open string…
We study the tropical lines contained in smooth tropical surfaces in R^3. On smooth tropical quadric surfaces we find two one-dimensional families of tropical lines, like in classical algebraic geometry. Unlike the classical case, however,…
We introduce adic tropicalizations for subschemes of toric varieties as limits of Gubler models associated to polyhedral covers of the ordinary tropicalization. Our main result shows that Huber's adic analytification of a subscheme of a…
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 explore physics on the boundary of a Randall-Sundrum type model when the brane tension is slightly sub-critical. We calculate the masses of the Kaluza-Klein decomposition of the graviton and use a toy model to show how localized gravity…
We study representations of tropical linear spaces as intersections of tropical hyperplanes of circuits. For several classes of matroids, we describe minimal tropical bases. We also show that every realizable tropical linear space has a…
Enumerative algebraic geometry deals with problems of counting geometric objects defined algebraically, An important class of enumerative problems is that of counting curves: given a class of curves in some projective variety defined by…
We construct a cosmological model based on a free particle model which is constrained on an embedded toroidal brane, with a general rotation around a specific axis in the bulk space. Some related issues such as the rotation axis of the…
In this paper we study tropicalization of Grassmannian and linear varieties. In particular, we study the tropical linear spaces cor- responding to the phylogenetic trees. We prove that corresponding to each subtree of the phylogenetic tree…
We study lifts of tropical bitangents to the tropicalization of a given complex algebraic curve together with their lifting multiplicities. Using this characterization, we show that generically all the seven bitangents of a smooth tropical…
We relate some features of Bruhat-Tits buildings and their compactifications to tropical geometry. If G is a semisimple group over a suitable non-Archimedean field, the stabilizers of points in the Bruhat-Tits building of G and in some of…
We study both A-type and B-type D-branes in the gauged linear sigma model by considering worldsheets with boundary. The boundary conditions on the matter and vector multiplet fields are first considered in the large-volume phase/non-linear…