Related papers: BPS states, knots and quivers
Knot theory provides a powerful tool for the understanding of topological matters in biology, chemistry, and physics. Here knot theory is introduced to describe topological phases in the quantum spin system. Exactly solvable models with…
We study the Chern-Simons partition function of orthogonal quantum group invariants, and propose a new orthogonal Labastida-Mari\~{n}o-Ooguri-Vafa conjecture as well as degree conjecture for free energy associated to the orthogonal…
We define and study a bigraded knot invariant whose Euler characteristic is the Alexander polynomial, closely connected to knot Floer homology. The invariant is the homology of a chain complex whose generators correspond to Kauffman states…
To speak about identical particles - bosons or fermions - in quantum field theories with kappa-deformed Poincare symmetry, one must have a kappa-covariant notion of particle exchange. This means constructing intertwiners of the relevant…
We consider a variety of physical systems in which one has states that can be thought of as generalised instantons. These include Yang--Mills theories on manifolds with a torsion-free $G$-structure, analogous gravitational instantons and…
It is known that knot homologies admit a physical description as spaces of open BPS states. We study operators and algebras acting on these spaces. This leads to a very rich story, which involves wall crossing phenomena, algebras of closed…
We describe the counting of BPS states of Type II strings on K3 by relating the supersymmetric cycles of genus $g$ to the number of rational curves with $g$ double points on K3. The generating function for the number of such curves is the…
We investigate the relation between local unitary symmetries and entanglement invariants of multi-qubit systems. The Hilbert space of such systems can be stratified in terms of states with different types of symmetry. We review the…
We make a precision test of a recently proposed conjecture relating Chern-Simons gauge theory to topological string theory on the resolution of the conifold. First, we develop a systematic procedure to extract string amplitudes from vacuum…
We consider a large class of branes in toric strip geometries, both non-periodic and periodic ones. For a fixed background geometry we show that partition functions for such branes can be reinterpreted, on one hand, as quiver generating…
We explicitly write down the invariant supersymmetry conditions for branes with generic values of moduli and U-duality charges in various space-time dimensions $D \leq 10$. We then use these results to obtain new BPS states, corresponding…
We study a three-dimensional gauge theory obtained from the dimensional reduction of a D4-brane worldvolume theory in the background of space-time moduli. An SL(3) symmetry in this theory, which acts on fields as well as coupling constants,…
In this paper we introduce a new invariant of virtual knots and links that is non-trivial for infinitely many virtuals, but is trivial on classical knots and links. The invariant is initially be expressed in terms of a relative of the…
We study the invariant of knots in lens spaces defined from quantum Chern-Simons theory. By means of the knot operator formalism, we derive a generalization of the Rosso-Jones formula for torus knots in L(p,1). In the second part of the…
We have found that kappa-symmetry allows a covariant quantization provided the ground state of the theory is strictly massive. For D-p-branes a Hamiltonian analysis is performed to explain the existence of a manifestly supersymmetric and…
Using recent results on BPS quiver theory, we develop a group theoretical method to describe the quiver mutations encoding the quantum mechanical duality relating the spectra of distinct quivers. We illustrate the method by computing the…
We obtain a quiver representation for a family of knots called double twist knots $K(p,-m)$. Particularly, we exploit the reverse engineering of Melvin-Morton-Rozansky(MMR) formalism to deduce the pattern of the charge matrix for these…
In Classical Knot Theory and in the new Theory of Quantum Invariants substantial effort was directed toward the search for unknotting moves on links. We solve, in this note, several classical problems concerning unknotting moves. Our…
Previous work of the author and N. Reshetikhin defines an invariant $\operatorname{Z}_{N}^{\psi}(K, \rho, \mu)$ of a knot $K$, a representation $\rho : \pi_{1}(S^{3} \setminus K) \to \operatorname{SL}_2(\mathbb{C})$, and a logarithm $\mu$…
We construct two distinct yet related M-theory models that provide suitable frameworks for the study of knot invariants. We then focus on the four-dimensional gauge theory that follows from appropriately compactifying one of these M-theory…