相关论文: Topological aspects of brane fields: solitons and …

Four-dimensional $\mathcal{N}=4$ supersymmetric Yang-Mills theory, at a point on the Coulomb branch where $SU(N)$ gauge symmetry is spontaneously broken to $SU(N-1)\times U(1)$, admits BPS solitons describing a spherical shell of electric…

Topological terms in the O(3) nonlinear sigma model in (1+1) and (2+1) dimensions are re-examined based on the description of the SU(2)-valued field $g$. We first show that the topological soliton term in (1+1) dimensions arises from the…

In this work we obtain topological and dual theories on brane-worlds in several dimensions. Our brane is a solitonic-like hypersurface embedded in a space-time with a specific dimensionality and it appears due to the breaking of a…

We use sheaves of spectra to quantize a Hamiltonian $\coprod\limits_n BO(n)$-action on $\varinjlim\limits_{N}T^*\mathbf{R}^N$ that naturally arises from Bott periodicity. We employ the category of correspondences developed in [GaRo] to give…

We study the classification of D-branes in all compact Lie groups including non-simply-laced ones. We also discuss the global structure of the quantum moduli space of the D-branes. D-branes are classified according to their positions in the…

We extend the definition of hopfions to include a class of spin-$h$ fields and use this to introduce the electromagnetic and gravitational hopfions of different algebraic types. The fields are constructed through the Penrose contour…

The various descent and duality relations among BPS and non-BPS D-branes are classified using topological K-theory. It is shown how the descent procedures for producing type-II D-branes from brane-antibrane bound states by tachyon…

The non-commutative geometry of a large auxiliary $B$-field simplifies the construction of D-branes as solitons in open string field theory. Similarly, fundamental strings are constructed as localized flux tubes in the string field theory.…

We obtain localized field configurations with finite energy in a ($2+1$)-dimensional model with Maxwell and Chern-Simons gauge terms coupled to a massive complex scalar field. These non-topological solitons are characterized by the $U(1)$…

We give a review of some recent work on the construction and classification of $p$-brane solutions in maximal supergravity theories in all dimensions $4\le D\le 11$. These solutions include isotropic elementary and solitonic $p$-branes,…

Using geometric arguments, we compute the group of homotopy classes of maps from a closed $(n+1)$-dimensional manifold to the $n$-sphere for $n \geq 3$. Our work extends results from Kirby, Melvin and Teichner for closed oriented…

We consider the topological and geometric structures associated with cohomological and homological objects in M-theory. For the latter, we have M2-branes and M5-branes, the analysis of which requires the underlying spacetime to admit a…

We study the Symmetry Topological Field Theory in holography associated with 4d $\mathcal{N}=1$ Super Yang-Mills theory with gauge algebra $\mathfrak{su}(M)$. From this, all the bulk symmetry operators are computed and matched to various…

Sigma models effectively describe ordered phases of systems with spontaneously broken symmetries. At low energies, field configurations fall into solitonic sectors, which are homotopically distinct classes of maps. Depending on context,…

We consider generalizations of symplectic manifolds called n-plectic manifolds. A manifold is n-plectic if it is equipped with a closed, nondegenerate form of degree n+1. We show that higher structures arise on these manifolds which can be…

We study a general configuration of parallel branes having co-dimension >2 situated inside a compact d-dimensional bulk space within the framework of a scalar and flux field coupled to gravity in D dimensions, such as arises in the bosonic…

We examine configurations of finite subsets of manifolds within the homotopy-theoretic context of $\infty$-categories by way of stratified spaces. Through these higher categorical means, we identify the homotopy types of such configuration…

We define Homotopy quantum field theories (HQFT) as Topological quantum field theories (TQFT) for manifolds endowed with extra structure in the form of a map into some background space X. We also build the category of homotopy cobordisms…

We examine the possibility that gauge field configurations on stacks of parallel Dp branes support topological solitons. We give an exhaustive list of possible soliton charges for p<7. We also discuss how configurations carrying the soliton…

We show that the topological charge of the n-soliton solution of the sine-Gordon equation n is related to the genus g > 1 of a constant negative curvature compact surface described by this configuration. The relation is n=2(g-1), where n is…