相关论文: Instanton-torus knot duality in 5d SQED and $SU(2)…
We discuss recently formulated instanton-torus knot duality in $\Omega$-deformed 5D SQED on $\mathbb{R}^4 \times S^1$ focusing at the microscopic aspects of the condensate formation in the instanton ensemble. Using the chain of dualities…
We establish the duality between the torus knot superpolynomials or the Poincar\'e polynomials of the Khovanov homology and particular condensates in $\Omega$-deformed 5D supersymmetric QED compactified on a circle with 5d Chern-Simons(CS)…
A torus-covering $T^2$-knot is a surface-knot of genus one determined from a pair of commutative braids. For a torus-covering $T^2$-knot $F$, we determine the number of irreducible metabelian $SU(2)$-representations of the knot group of $F$…
We show that for a torus knot the SL(2;C) Chern-Simons invariants and the SL(2;C) twisted Reidemeister torsions appear in an asymptotic expansion of the colored Jones polynomial. This suggests a generalization of the volume conjecture that…
We derive a closed-form expression for the adjoint polynomials of torus knots and investigate their special properties. The results are presented in the very explicit double sum form and provide a deeper insight into the structure of…
Every torus knot can be represented as a Fourier-(1,1,2) knot which is the simplest possible Fourier representation for such a knot. This answers a question of Kauffman and confirms the conjecture made by Boocher, Daigle, Hoste and Zheng.…
Invariant polynomials for torus links are obtained in the framework of the Chern-Simons topological gauge theory. The polynomials are computed as vacuum expectation values on the three-sphere of Wilson line operators representing the…
We calculate the twisted Reidemeister torsion of the complement of an iterated torus knot associated with a representation of its fundamental group to the complex special linear group of degree two. We also show that the twisted…
We study the relation between class S theories on punctured tori and isomonodromic deformations of flat SL(N) connections on the two dimensional torus with punctures. Turning on the self dual $\Omega$-background corresponds to a…
The quantum torus algebra plays an important role in a special class of solutions of the Toda hierarchy. Typical examples are the solutions related to the melting crystal model of topological strings and 5D SUSY gauge theories. The quantum…
Using the Nahm transform we investigate doubly periodic charge one SU(2) instantons with radial symmetry. Two special points where the Nahm zero modes have softer singularities are identified as the locations of instanton core constituents.…
The circle compactification of the 6-dim (2,0) superconformal theory of $A_{N-1}$ type leads the 5-dim SU(N) maximally supersymmetric gauge theory. Instanton solitons embody Kaluza-Klein modes and are conjectured to be composed of partonic…
There are several knot invariants in the literature that are defined using singular instantons. Such invariants provide strong tools to study the knot group and give topological applications. For instance, it gives powerful tools to study…
We consider the torus compactifications with flux of a class of $6d$ $(1,0)$ SCFTs that can be engineered as the low-energy theories on M$5$-branes near an M$9$-plane on a $C^2/Z_2$ singularity. Specifically, we concentrate on the two SCFTs…
A generalization of the volume conjecture relates the asymptotic behavior of the colored Jones polynomial of a knot to the Chern--Simons invariant and the Reidemeister torsion of the knot complement associated with a representation of the…
We study various cases of dualities between $\cal{N}$$=1$ 5d supersymmetric gauge theories. We motivate the dualities using brane webs, and provide evidence for them by comparing the superconformal index. In many cases we find that the…
Five and six dimensional SUSY gauge theories, with one or two compactified directions, are discussed. The 5d theories with the matter hypermultiplets in the fundamental representation are associated with the twisted $XXZ$ spin chain, while…
Gauge theories in four dimensions can exhibit interesting low energy phenomena, such as infrared enhancements of global symmetry. We explore a class of 4d N=1 gauge theories arising from a construction that is motivated by duality walls in…
We study the $3d$ $\mathcal{N}=2$ theories resulting from the compactification of a family of $5d$ SCFTs on a torus with flux in the global symmetry. The family of $5d$ SCFTs used in the analysis is the one that UV completes the $5d$…
We numerically examine the self-dual solutions of self-intersecting strings immersed in four dimensions. We find that open torus knots have topologies that can support monopole/anti-monopole as well as q-qbar production and annihilation. We…