Related papers: Abrikosov Vortex and Branes
We study a field-theoretical analogue of the Aharonov-Bohm effect in two-, three- and four-dimensional Abelian Higgs models; the corresponding topological interaction is proportional to the linking number of the Abrikosov vortex and the…
With the perspective of looking for experimentally detectable physical applications of the so-called topological embedding, a procedure recently proposed by the author for quantizing a field theory around a non-discrete space of classical…
Electrodynamic phenomena related to vortices in superconductors have been studied since their prediction by Abrikosov, and seem to hold no fundamental mysteries. However, most of the effects are treated separately, with no guiding…
There is an interpretation of open string field theory in algebraic topology. An interpretation of closed string field theory can be deduced from this open string theory to obtain as well the interpretation of open and closed string field…
We explore possibilities and limitations of a purely topological approach to the Dvoretzky Theorem.
Through the question of singular topologies in the Boulatov model, we illustrate and summarize some of the recent advances in Group Field Theory.
The paper contains the construction of a topological quantum field theory with corners that underlies the smooth topological quantum field theory of Lickorish. Among other things, a contraction formula for diagrams is proved, the presence…
We describe a topological field theory that studies the moduli space of solutions of the symplectic vortex equations. It contains as special cases the topological sigma-model and topological Yang-Mills over Kahler surfaces. The correlation…
At high temperatures the A_0 component of the Yang--Mills field plays the role of the Higgs field, and the 1-loop potential V(A_0) plays the role of the Higgs potential. We find a new stable vortex solution of the Abrikosov-Nielsen-Olesen…
The equations for topological fields in the $4d$ higher spin theory are considered. It is shown that these fields contain a finite number of degrees of freedom that justifies their naming. The issue of construction of gauge invariant…
We survey some results on real rational surfaces focused on their topology and their birational geometry.
We present topological features of the magnetic response (orbital and spin) of a two-dimensional degenerate and non interacting electron gas due to inhomogeneous applied magnetic fields. These issues are analysed from the point of view of…
In this paper we start with the applications of polyfold theory to symplectic field theory.
It is shown that the SO(3) gauge field configurations can be completely characterised by certain gauge invariant vector fields. The singularities of these vector fields describe the topological aspects of the gauge field configurations. The…
We consider the non-relativistic Chern-Simons equations proposed by Zhang, Hansen and Kivelson as the mean field theory of the fractional Hall effect. We prove the existence of the vortex lattice solutions (i.e. solution with lattice…
A mathematically rigorous Hamiltonian formulation for classical and quantum field theories is given. New results include clarifications of the structure of linear fields, and a plausible formulation for nonlinear fields. Many mathematical…
Over a large class of function fields, we show that the solutions of some linear equations in the topological closure of a certain subgroup of the group of units in the function field are exactly the solutions that are already in the…
Structures in low-dimensional topology and low-dimensional geometry -- often combined with ideas from (quantum) field theory -- can explain and inspire concepts in algebra and in representation theory and their categorified versions. We…
In this expository paper we introduce extended topological quantum field theories and the cobordism hypothesis.
Recently, a topological field theory of membrane-matter coupled to BF theory in arbitrary spacetime dimensions was proposed [1]. In this paper, we discuss various aspects of the four-dimensional theory. Firstly, we study classical solutions…