Related papers: Refined Hopf Link Revisited
Using the shuffle structure of the graphs, we introduce a new kind of the Hopf algebraic structure for tagged graphs with, or without loops. Like a quantum group structure, its product is non-commutative. With the help of the Hopf algebraic…
The $\mathrm{U}(1)$ Chern-Simons theory can be extended to a topological $\mathrm{U}(1)^n$ theory by taking a combination of Chern-Simons and BF actions, the mixing being achieved with the help of a collection of integer coupling constants.…
We find a direct relation between quiver representation theory and open topological string theory on a class of toric Calabi-Yau manifolds without compact four-cycles, also referred to as strip geometries. We show that various quantities…
In his work on P-partitions, Stembridge defined the algebra of peak functions Pi, which is both a subalgebra and a retraction of the algebra of quasi-symmetric functions. We show that Pi is closed under coproduct, and therefore a Hopf…
We establish connectedness criteria for graphs associated to monomials in certain quotients of the mod 2 dual Steenrod algebra. We also investigate questions about trees and Hamilton cycles in the context of these graphs. Finally, we…
We solve the $K$-theoretically refined Donaldson-Thomas theory of local curves. Our results avoid degeneration techniques, but rather exploit direct localisation methods to reduce the refined Donaldson-Thomas partition function to the…
We prove that topological recursion applied to the spectral curve of colored HOMFLY-PT polynomials of torus knots reproduces the n-point functions of a particular partition function called the extended Ooguri-Vafa partition function. This…
In this work, we study a class of higher derivative couplings in the string effective action arising at the junction of topological string theory and supersymmetric gauge theories in the $\Omega$-background. They generalise a series of…
In Part I of this paper, we have used spectral submanifold (SSM) theory to construct reduced-order models for harmonically excited mechanical systems with internal resonances. In that setting, extracting forced response curves formed by…
In our continued efforts of matching full string computations with the corresponding effective field theory computations, we evaluate string theory correlators in closed forms. In particular, we consider a correlator between three SYM…
In this paper we analyze the quantum homological invariants (the Poincar\'e polynomials of the $\mathfrak{sl}_N$ link homology). In the case when the dimensions of homologies of appropriate topological spaces are precisely known, the…
The Hamiltonian analysis for the Chern-Simons theory and Pontryagin invariant, which depends of a connection valued in the Lie algebra of SO(3,1), is performed. By applying a pure Dirac's method we find for both theories the extended…
We present an invariant of connected and oriented closed 3-manifolds based on a coribbon Weak Hopf Algebra H with a suitable left-integral. Our invariant can be understood as the generalization to Weak Hopf Algebras of the…
For our own education, we reconstruct the Hopf algebra of Connes and Moscovici obtained by the action of vector fields on a crossed product of functions by diffeomorphisms. We extend the realization of that Hopf algebra in terms of rooted…
We consider the moduli space of flat connections on the Riemann surface with marked points. The new efficient parametrization is suggested and used to construct an integrable model on the moduli space. A family of commuting Hamiltonians is…
We study the connection between topological strings and contact homology recently proposed in the context of knot invariants. In particular, we establish the proposed relation between the Gromov-Witten disk amplitudes of a Lagrangian…
We find approximations by Vassiliev invariants for the coefficients of the Jones polynomial and all specializations of the HOMFLY and Kauffman polynomials. Consequently, we obtain approximations of some other link invariants arising from…
We show how the Hopf algebra of rooted trees encodes the combinatorics of Epstein-Glaser renormalization and coordinate space renormalization in general. In particular we prove that the Epstein-Glaser time-ordered products can be obtained…
We compute the correlation of the net baryon number with the electric charge ($\chi_{BQ}$) for an interacting hadron gas using the S-matrix formulation of statistical mechanics. The observable $\chi_{BQ}$ is particularly sensitive to the…
The Coulomb branch indices of Argyres-Douglas theories on $L(k,1)\times S^{1}$ are recently identified with matrix elements of modular transforms of certain $2d$ vertex operator algebras in a particular limit. A one parameter generalization…