Related papers: On Universal Eigenvalues of Casimir Operator
In this paper, the decomposition of SU(2) gauge potential in terms of Pauli spinors is studied. Using this decomposition, the spinor strutures of the Chern-Simons form and the Chern density are obtained. Furthermore, by these spinor…
We represent a general bilinear Calder\'on-Zygmund operator as a sum of simple dyadic operators. The appearing dyadic operators also admit a simple proof of a sparse bound. In particular, the representation implies a so called sparse T1…
We give the definition of a duality that is applicable to arbitrary $k$-forms. The operator that defines the duality depends on a fixed form $\Omega$. Our definition extends in a very natural way the Hodge duality of $n$-forms in $2n$…
Classical and quantum superintegrable systems have a long history and they possess more integrals of motion than degrees of freedom. They have many attractive properties, wide applications in modern physics and connection to many domains in…
The universal Vassiliev invariant from the perturbative Chern-Simons theory is actually a knot invariant without any correction term. The anomaly considered by Bott and Taubes is proved to be zero.
Based on the superconformal algebra we construct a dual operator that introduces a grading among bosonic generators independent of the boson/fermion grading of the superalgebra. This dual operator allows us to construct an action that is…
Given a semidirect product $\frak{g}=\frak{s}\uplus\frak{r}$ of semisimple Lie algebras $\frak{s}$ and solvable algebras $\frak{r}$, we construct polynomial operators in the enveloping algebra $\mathcal{U}(\frak{g})$ of $\frak{g}$ that…
By employing the multilevel algorithm in numerical Monte Carlo simulations, we evaluate the static potential in four dimensional SU(2) lattice gauge theory with no dynamical fermions, for static sources in the j=1/2,1,3/2 representations.…
There is significant evidence for a duality between (non-supersymmetric) U(N) Chern-Simons theories at level k coupled to fermions, and U(k) Chern-Simons theories at level N coupled to scalars. Most of the evidence comes from the large N 't…
We investigate the curvature operator of the second kind on product Riemannian manifolds and obtain some optimal rigidity results. For instance, we prove that the universal cover of an $n$-dimensional non-flat complete locally reducible…
In this paper we study the algebra of quantum observables of the Chern-Simons matrix model which was originally proposed by Susskind and Polychronakos to describe electrons in fractional quantum Hall effects. We establish the commutation…
We represent in the universal form restricted one-instanton partition function of supersymmetric Yang-Mills theory. It is based on the derivation of universal expressions for quantum dimensions (universal characters) of Cartan powers of…
Polynomial representations of general linear groups and modules over Schur algebras are compared. We work over an arbitrary commutative ring and show that Schur-Weyl duality is the key for an equivalence between both categories.
We introduce the most general quartic Poisson algebra generated by a second and a fourth order integral of motion of a 2D superintegrable classical system. We obtain the corresponding quartic (associative) algebra for the quantum analog and…
We prove the existence of $\mathrm{GSpin}_{2n}$-valued Galois representations corresponding to cohomological cuspidal automorphic representations of certain quasi-split forms of $\mathrm{GSO}_{2n}$ under the local hypotheses that there is a…
A general classification of linear differential and finite-difference operators possessing a finite-dimensional invariant subspace with a polynomial basis (the generalized Bochner problem) is given. The main result is that any operator with…
Abelian Chern-Simons gauge theory is known to possess a `$S$-self-dual' action where its coupling constant $k$ is inverted {\it i.e.} $k \leftrightarrow {1 \over k}$. Here a vector non-abelian duality is found in the pure non-abelian…
It is well-known that the SU(2) quantum Racah coefficients or the Wigner $6j$ symbols have a closed form expression which enables the evaluation of any knot or link polynomials in SU(2) Chern-Simons field theory. Using isotopy equivalence…
In this article we study the action of the non-planar two-loop dilatation operator in an SU(2)*SU(2) sub-sector of the ABJ Chern-Simons-matter theory. The gauge invariant operators we consider are the restricted Schur polynomials. As in…
A new universal model to implement the Seiberg-Witten approach to low-energy properties of the supersymmetric N=2 gauge theory with an arbitrary compact simple gauge group, classical or exceptional, is suggested. It is based on the…