相关论文: Abrikosov Vortex and Branes

We present a finite energy topological Z(2) vortex solution in a 2+1 dimensional SO(3) gauge field theory minimally coupled to a matrix valued Higgs field. The vortex carries a Z(2) magnetic charge and obeys a modulo two addition property.…

This is a survey of the theory of real trees and their applications.

This is a brief review of my work on the correspondence between four-dimensional $\mathcal{N} = 1$ supersymmetric field theories realized by brane tilings and two-dimensional integrable lattice models. I explain how to construct integrable…

Using a Zariski topology associated to a finite field extensions, we give new proofs and generalize the primitive and normal basis theorems.

We prove existence of Abrikosov vortex lattice solutions of the Ginzburg-Landau equations in two dimensions, for magnetic fields larger than but close to the first critical magnetic field.

In this paper we give an overview of different Morse-theoretic methods used to study the topology of moduli spaces of Higgs bundles.

These notes are an introduction to higher dimensional local fields and higher dimensional adeles. As well as the foundational theory, we summarise the theory of topologies on higher dimensional local fields and higher dimensional local…

We report on some recent results on a class of relativistic lagrangian field theories supporting non-topological soliton solutions and their applications in the contexts of Gravitation and Cosmology. We analyze one and many-components…

We show that it is possible to formulate Abelian Chern-Simons theory on a lattice as a topological field theory. We discuss the relationship between gauge invariance of the Chern-Simons lattice action and the topological interpretation of…

This is a survey of various types of Floer theories (both in symplectic geometry and gauge theory) and relations among them.

We describe some instances of the appearance of Chern's mathematical ideas in physics. By means of simple examples, we bring out the geometric and topological ideas which have found application in describing the physical world. These…

We extend our sum over topologies formula to fermions. We show that fermionic fields display an instability with respect to topology fluctuations. We present some phenomenological arguments for a modification of the action in the case of…

In this survey we present several results concerning various topologies that were introduced in recent years on spaces of valuation domains.

See hep-ph/0304045

We survey some results on toric topology.

Suggestions concerning the generalization of the geometric quantization to the case of nonlinear field theories are given. Results for the Liouville field theory are presented.

A new technique is proposed to classify a topological field in abelian lattice gauge theories. We perform the classification by regarding the topological field as a local composite field of the gauge field tensor instead of the vector…

In this talk I describe a recently introduced field-theoretical approach that can be used as an alternative framework to study one-dimensional systems of highly correlated particles.

We characterize the Zariski topologies over an algebraically closed field in terms of general dimension-theoretic properties. Some applications are given to complex manifold and to strongly minimal sets.

A short survey on applications of algebraic geometry in topological data analysis.