相关论文: Loop groups, anyons and the Calogero-Sutherland mo…

We construct the classical W-algebras for some non-abelian Toda systems associated with the Lie groups GL(2n,R) and Sp(n,R). We start with the set of characteristic integrals and find the Poisson brackets for the corresponding Hamiltonian…

We develop a method to compute the one-loop effective action of noncommutative U(1) gauge theory based on the bosonic worldline formalism, and derive compact expressions for N-point 1PI amplitudes. The method, resembling perturbative string…

In the recent years a lot of effort has been made to extend the theory of hyperholomorphic functions from the setting of associative Clifford algebras to non-associative Cayley-Dickson algebras, starting with the octonions. An important…

We consider the quantum mechanics of Calogero models in an oscillator or Coulomb potential on the N-dimensional sphere. Their Hamiltonians are obtained by an appropriate Dunkl deformation of the oscillator/Coulomb system on the sphere and…

The BC-type Calogero-Sutherland model (CSM) is an integrable extension of the ordinary A-type CSM that possesses a reflection symmetry point. The BC-CSM is related to the chiral classes of random matrix ensembles (RMEs) in exactly the same…

We study the $SU(N)$, level $1$ Wess-Zumino-Witten model, with affine primary fields as spinon fields of fundamental representation. By evaluating the action of the Yangian generators $Q_{0}^{a}, Q_{1}^{a}$ and the Hamiltonian $H_2$ on two…

We compute euclidean coordinate space correlation functions in a holographic model of QCD. We concentrate, in particular, on channels that are related to the U(1)_A problem, the flavor-singlet axialvector, pseudoscalar meson, and…

We construct complex root spaces remaining invariant under antilinear involutions related to all Coxeter groups. We provide two alternative constructions: One is based on deformations of factors of the Coxeter element and the other based on…

q-bosonic realization of the underlying Yang-Baxter algebra is identified for a series of quantum integrable systems, including some new models like two-mode q-bosonic model leading to a coupled two-component derivative NLS model, wide…

This paper investigates the connection between braid group representations, defect operators, and holography within the AdS/CFT framework. It focuses on the correspondence between bulk Wilson loops and boundary defect operators, emphasizing…

Supersymmetric circular Wilson loops in $\mathcal{N}=4$ Super-Yang-Mills theory are discussed starting from their Gaussian matrix model representations. Previous results on the generating functions of Wilson loops are reviewed and extended…

We construct generalizations of the Calogero-Sutherland-Moser system by appropriately reducing a model involving many unitary matrices. The resulting systems consist of particles on the circle with internal degrees of freedom, coupled…

We make progress towards a derivation of a low energy effective theory for SU(2) Yang-Mills theory. This low energy action is computed to 1-loop using the renormalization group technique, taking proper care of the Slavnov-Taylor identities…

We study a conformal field theory that arises in the infinite-volume limit of a spin chain with $U_q(sl_2)$ global symmetry. Most operators in the theory are defect-ending operators which allows $U_q(sl_2)$ symmetry transformations to act…

We describe the construction of quantum gates (unitary operators) from boolean functions and give a number of applications. Both non-reversible and reversible boolean functions are considered. The construction of the Hamilton operator for a…

It is well known through a recent work of Bernard, Gaudin, Haldane and Pasquier (BGHP) that the usual spin Calogero-Sutherland (CS) model, containing particles with $M$ internal degrees of freedom, respects the $Y(gl_M)$ Yangian symmetry.…

In this paper we introduce a one-dimensional model of $su(2)_k$ anyons in which the number of anyons can fluctuate by means of a pairing term. The model can be tuned to a point at which one can determine the exact zero-energy ground states,…

This is an outline of Erlangen Program at Large. Study of objects and properties, which are invariant under a group action, is very fruitful far beyond the traditional geometry. In this paper we demonstrate this on the example of the group…

We construct Hamiltonians for systems of nonrelativistic particles linearly coupled to massive scalar bosons using abstract boundary conditions. The construction yields an explicit characterisation of the domain of self-adjointness in terms…

A certain generalization of the algebra $gl(N,{\bf R})$ of first-order differential operators acting on a space of inhomogeneous polynomials in ${\bf R}^{N-1}$ is constructed. The generators of this (non)Lie algebra depend on permutation…