Related papers: $({\mathfrak{gl}}_M, {\mathfrak{gl}}_N)$-Dualities…

We prove an equivalence between the actions of the Gaudin algebras with irregular singularities for $\mathfrak{gl}_d$ and $\mathfrak{gl}_{p+m|q+n}$ on the Fock space of $d(p+m)$ bosonic and $d(q+n)$ fermionic oscillators. This establishes a…

We establish a duality of the non-periodic Gaudin model associated with superalgebra $\mathfrak{gl}_{m|n}$ and the non-periodic Gaudin model associated with algebra $\mathfrak{gl}_k$. The Hamiltonians of the Gaudin models are given by…

The T-duality symmetries of a family of two-dimensional massive integrable field theories defined in terms of asymmetric gauged Wess-Zumino-Novikov-Witten actions modified by a potential are investigated. These theories are examples of…

We review the general formalism of duality rotations for $\cal N$-extended (super)conformal gauge multiplets of arbitrary (super)spin in four dimensions, with ${\cal N} \geq 0$. Self-dual models for a vector field (${\cal N}=0$) and for…

We describe the large $N$ limit of spectral duality between rational Gaudin models introduced by Adams, Harnad and Hurtubise. The limit of the ${\rm gl}_N$ model is performed by means of a noncommutative torus algebra represented by the…

It is shown, at the level of the classical action, that the Wess-Zumino-Witten-Novikov model is equivalent to a combined BF theory and a Chern-Simons action in the presence of a unique boundary term. This connection relies on the techniques…

We give a geometric realization of the symmetric algebra of the tensor space $C^n \bigotimes C^m$ together with the action of the dual pair $(gl_n, gl_m)$ in terms of lagrangian cycles in the cotangent bundles of certain varieties. We…

We study the large $N$ limit of the spectral duality between the classical $\mathfrak{gl}_M$ XXX spin chain and the $\mathfrak{gl}_N$ trigonometric Gaudin model in its rational reduced form. The infinite-dimensional limit of the Gaudin…

We extend duality between the quantum integrable Gaudin models with boundary and the classical Calogero-Moser systems associated with root systems of classical Lie algebras $B_N$, $C_N$, $D_N$ to the case of supersymmetric ${\rm gl}(m|n)$…

We describe non-Abelian T-dualities for $\mathcal{N} = 2$ two dimensional gauged linear sigma model (GLSM). We start with the case of left and right $(2, 2)$ supersymmetry (SUSY), $U(1)$ gauge group, and global non-Abelian symmetries. Our…

We show that the images of the Bethe subalgebras of the Yangians $Y(\mathfrak{gl}_{n})$ and $Y(\mathfrak{gl}_{m})$ under the homomorphisms to $U(\mathfrak{gl}_{n+m})$ given by the Olshanski centralizer construction coincide. We use this…

We revisit universal features of duality in linear and nonlinear relativistic scalar and Abelian 1-form theories with single or multiple fields, which exhibit ordinary or generalized global symmetries. We show that such global symmetries…

Duality symmetries of supergravity theories are powerful tools to restrict the number of possible actions, to link different dimensions and number of supersymmetries and might help to control quantisation. (Hodge-Dirac-)Dualisation of gauge…

We study the dualities for sigma models with fermions and bosons. We found that the generalization of the SO(m,m) duality for D=2 sigma models and the Sp(2n) duality for D=4 sigma models is the orthosymplectic duality OSp(m,m|2 n). We study…

The problem of quantum equivalence between non-linear sigma models related by Abelian or non-Abelian T-duality is studied in perturbation theory. Using the anomalous Ward identity for Weyl symmetry we derive a relation between the Weyl…

We develop a general formalism of duality rotations for bosonic conformal spin-$s$ gauge fields, with $s\geq 2$, in a conformally flat four-dimensional spacetime. In the $s=1$ case this formalism is equivalent to the theory of…

Let $M$ be a tensor product of unitarizable irreducible highest weight modules over the Lie (super)algebra $\mathcal{G}$, where $\mathcal{G}$ is $\mathfrak{gl}(m|n)$, $\mathfrak{osp}(2m|2n)$ or $\mathfrak{spo}(2m|2n)$. We show, using super…

In a recent publication a procedure was developed which can be used to derive completely gauge invariant models from general Lagrangian densities with $N$ order of derivatives and $M$ rank of tensor potential. This procedure was then used…

In this paper, we generalize the duality between self-dual and Maxwell-Chern-Simons theories for the case of a CPT-even Lorentz-breaking extension of these theories. The duality is demonstrated with use of the gauge embedding procedure,…

On a Fock space constructed from $mn$ free bosons and lattice ${\Bbb {Z}}^{mn}$, we give a level $n$ action of the quantum toroidal algebra $\mathscr {E}_m$ associated to $\mathfrak{gl}_m$, together with a level $m$ action of the quantum…