相关论文: SU(3) instanton homology for webs and foams
Suppose $(M, \gamma)$ is a balanced sutured manifold and $K$ is a rationally null-homologous knot in $M$. It is known that the rank of the sutured Floer homology of $M\backslash N(K)$ is at least twice the rank of the sutured Floer homology…
We introduce two invariants called sl(3) Khovanov module and pointed sl(3) Khovanov homology for spatial webs (bipartite trivalent graphs). Those invariants are related to Kronheimer-Mrowka's instanton invariants $J^\sharp$ and $I^\sharp$…
We review the SO(3) instanton gauge theory of Fintushel and Stern and recast it in the context of 4-manifolds with cylindrical ends. Appli- cations to the Z/2-homology cobordism group of Z/2-homology 3-spheres are given.
The continued development of models that propose the existence of fractional topological objects in the Yang-Mills vacuum has called for a quantitative method to study the topological structure of $\mathrm{SU}(N)$ gauge theory. We present…
The SU(3)-Casson invariant for integral homology 3-spheres as studied by Boden-Herald possesses a 'spectral flow obstruction' to being an integer valued invariant which depends only on the non-degenerate (perturbed) moduli space of flat…
This is the first in a series of papers exploring the relationship between the Rohlin invariant and gauge theory. We discuss the Casson-type invariant of a 3-manifold with the integral homology of a torus, given by counting projectively…
We calculate instanton corrections to three dimensional gauge theories with N=4 and N=8 supersymmetry and SU(n) gauge groups. The N=4 results give new information about the moduli space of n BPS SU(2) monopoles, including the leading order…
We use annular foam TQFTs introduced by the first two authors to define equivariant $SL(2)$ and $SL(3)$ web algebras in the annulus. To a diagram of a tangle in the thickened annulus we assign a complex of bimodules over these algebras…
Knots and links in 3-manifolds are studied by applying intersection invariants to singular concordances. The resulting link invariants generalize the Arf invariant, the mod 2 Sato-Levine invariants, and Milnor's triple linking numbers.…
We study self-dual SU(N) gauge field configurations on the 4 torus with twisted boundary conditions, known as fractional instantons. Focusing on the minimum non-zero action case, we generalize the constant field strength solutions…
We construct the universal sl(2)-tangle cohomology using an approach with webs and dotted foams. This theory depends on two parameters, and for the case of links it is a categorification of the unnormalized Jones polynomial of the link.
Equivariant singular instanton Floer theory is a framework that associates to a knot in an integer homology 3-sphere a suite of homological invariants that are derived from circle-equivariant Morse-Floer theory of a Chern-Simons functional…
A specific algebraic coupling model involving multiple quantization axes is presented in which previously indistinguishable SU(2) symmetry groups become distinguishable when coupled into a SU(3) group structure. The model reveals new…
The group SU(3) is parameterized in terms of generalized ``Euler angles''. The differential operators of SU(3) corresponding to the Lie Algebra elements are obtained, the invariant forms are found, the group invariant volume element is…
We use lattice simulations to study SU(3) gauge theory with 13 massless fermions in the fundamental representation. We present evidence that the theory is conformal with a non-zero infrared fixed point in the gauge coupling. We use a…
A method to obtain explicit and complete topological solution of SU(2) Chern-Simons theory on $S^3$ is developed. To this effect the necessary aspects of the theory of coloured-oriented braids and duality properties of conformal blocks for…
Motivated by the recent experimental success in realizing synthetic spin-orbit coupling in ultracold atomic systems, we consider N-component atoms coupled to a non-Abelian SU(N) gauge field. More specifically, we focus on the case, referred…
A spectral sequence is established, whose $E_{2}$ page is Bar-Natan's variant of Khovanov homology and which abuts to a deformation of instanton homology for knots and links. This spectral sequence arises as a specialization of a spectral…
In this paper the author discuss the relation between Lagrangian Floer homology and Gauge-theory (Donaldson theory) Floer homology. It can be regarded as a version of Atiyah-Floer type conjecture in the case of $SO(3)$-bundle with…
At fine lattice spacings, lattice simulations are plagued by slow (topological) modes that give rise to large autocorrelation times. These, in turn, lead to statistical and systematic errors that are difficult to estimate. We study the…