Related papers: Fivebranes and Knots
The altenating knots, links and twists projected on the S_2 sphere are identified with the phase Space of a Hamiltonian dynamic system of one degree of freedom. The saddles of the system correspond to the crossing points, the edges, to the…
I provide two solutions to the problem of categorifying quantum link invariants, which work uniformly for all gauge groups and originate in geometry and string theory. The first is based on a category of equivariant B-type branes on ${\cal…
We study D=3 field theories on the D3-branes stretched between two NS5-branes with NS B-field background. The theory is a noncommutative gauge theory. The mirror symmetry and S-duality of the theory are discussed. A new feature is that the…
We define an invariant of transverse links in the standard contact 3-sphere as a distinguished element of the Khovanov homology of the link. The quantum grading of this invariant is the self-linking number of the link. For knots, this gives…
Geometrically non-Higgsable seven-branes carry gauge sectors that cannot be broken by complex structure deformation, and there is growing evidence that such configurations are typical in F-theory. We study strongly coupled physics…
We present a number of investigations of 5d ${\cal N}=1$ supersymmetric gauge theories that make use of 5-brane web constructions and the 5d superconformal index. These include an observation of enhanced global symmetry in the 5d fixed…
In this paper we discuss two aspects of duality transformations on the Neveu-Schwarz (NS) 5-brane solutions in type II and heterotic string theories. First we demonstrate that the non-extremal NS 5-brane background is U-dual to its CGHS…
We try to give a geometric construction for 3d $\mathcal{N}=2$ gauge theories using three-manifolds and Dehn surgeries. We follow the story that wrapping M5-branes on plumbing three-manifolds leads to 3d theories with mixed Chern-Simons…
This paper begins with a survey of some applications of Khovanov homology to low-dimensional topology, with an eye toward extending these results to $\mathfrak{sl}(n)$ homologies. We extend Levine and Zemke's ribbon concordance obstruction…
We consider Wilson loop observables for Chern-Simons theory at large N and its topological string dual and extend the previous checks for this duality to the case of links. We find an interesting structure involving representation/spin…
Using the relation between Khovanov homology and the Heegaard Floer homology of branched double covers, we show how Khovanov homology can be used to establish tightness of branched double covers of certain transverse knots. We give examples…
We consider the tensor theory on coincident E8 5-branes compactified on a three torus. Using string theory, we predict that there must be distinct components in the moduli space of this theory.We argue that new superconformal field theories…
Witten's approach to Khovanov homology of knots is based on the five-dimensional system of partial differential equations, which we call Haydys-Witten equations. We argue for a one-to-one correspondence between its solutions and solutions…
Topological gauge theories in four dimensions which admit surface operators provide a natural framework for realizing homological knot invariants. Every such theory leads to an action of the braid group on branes on the corresponding moduli…
A homological invariant of 3-manifolds is defined, using abelian Yang-Mills gauge theory. It is shown that the construction, in an appropriate sense, is functorial with respect to the families of 4-dimensional cobordisms. This construction…
The Jones polynomial is a famous link invariant that can be defined diagrammatically via a skein relation. Khovanov homology is a richer link invariant that categorifies the Jones polynomial. Using spectral sequences, we obtain a skein-type…
We describe rules for computing a homology theory of knots and links in $\mathbb{R}^3$. It is derived from the theory of framed BPS states bound to domain walls separating two-dimensional Landau-Ginzburg models with (2,2) supersymmetry. We…
We describe a simple method for generating new string solutions for which the brane worldvolume is a curved space. As a starting point we use solutions with NS-NS charges combined with 2-d CFT's representing different parts of space-time.…
Coupling of a membrane and a five-brane to the bosonic sector of D=11 supergravity is considered. The five--brane is a dyonic object which carries both an electric and a magnetic charge of the D=11 three-form gauge field $A^3$, and it…
This is the first of a series of two technical papers devoted to the analysis of holonomy invariants in strict higher gauge theory with end applications in higher Chern--Simons theory. For a flat 2--connection, we define the 2-holonomy of…