Related papers: Quadratic Duality for Chiral Algebras
This paper extends previous work on linear correlations of representation functions of positive definite binary quadratic forms to allow indefinite forms.
The note complements topological aspects of the theory of chiral algebras.
We describe a new algebraic structure of "deformed chiral algebra" motivated by the study of the deformed W-algebras. We use it to gain some insights into the deformed Virasoro algebra.
The paper consists of two parts. In the first, we describe a way of getting from an algebra of chiral differential operators (cdo) on an abelian variety a cdo on the dual variety. The second is an introduction to the sigma-model on a torus…
Duality between the coloured quantum group and the coloured quantum algebra corresponding to GL(2) is established. The coloured L^{\pm} functionals are constructed and the dual algebra is derived explicitly. These functionals are then…
Following the formuation of Borcherds, we develop the theory of (quantum) vertex algebras, including several concrete examples. We also investigate the relationship between the vertex algebra and the chiral algebra due to Beilinson and…
For the chiral oscillator described by a second order and degenerate Lagrangian with special Euclidean group of symmetries, we show, by cotangent bundle Hamiltonian reduction, that reduced equations are Lie-Poisson on dual of oscillator…
We study recently proposed chiral higher spin theories - cubic theories of interacting massless higher spin fields in four-dimensional flat space. We show that they are naturally associated with gauge algebras, which manifest themselves in…
While quark-hadron duality is well-established experimentally, the current theoretical understanding of this important phenomenon is quite limited. To expose the essential features of the dynamics behind duality, we use a simple model in…
We establish a Schur type duality between a coideal subalgebra of the quantum group of type A and the Hecke algebra of type B with 2 parameters. We identify the $\imath$-canonical basis on the tensor product of the natural representation…
We show that Seiberg-like duality of $\mathcal{N}=1$ gauge theory coupled with tensor chiral fields and fundamental chiral fields works if the meson spectrum built from the tensor fields takes particular form: a) It should be truncated; b)…
A notion of dual curve for pseudoholomorphic curves in 4--manifolds turns out to be possible only if the notion of almost complex structure structure is slightly generalized. The resulting structure is as easy (perhaps easier) to work with,…
The duality symmetry of free electromagnetic field is analyzed within an algebraic approach. To this end, the conformal $c(1,3)$ algebra generators are expressed as operators quadratic in some abstract operators $\kappa^\alpha$ and…
Celestial holography suggests, among other things, that collinear singularities of graviton scattering amplitudes are described by the OPEs of some putative dual CFT. One of the great successes has been the insight that this duality is true…
We describe a method for evaluating chiral gauge theories that is not plagued by the doubling problem. To demonstrate the efficiency of the approach, we apply our ideas to the chiral Schwinger model.
This work addresses some relevant characteristics and properties of $q$-generalized associative algebras and $q$-generalized dendriform algebras such as bimodules, matched pairs. We construct for the special case of $q=-1$ an…
Double field theory was developed by theoretical physicists as a way to encompass $T$-duality. In this paper, we express the basic notions of the theory in differential-geometric invariant terms, in the framework of para-Kaehler manifolds.…
We establish an explicit isomorphism between the associated graded of the filtered chiral operad and the classical operad, which is useful for computing the cohomology of vertex algebras.
De Vries duality yields a dual equivalence between the category of compact Hausdorff spaces and a category of complete Boolean algebras with a proximity relation on them, known as de Vries algebras. We extend de Vries duality to completely…
We introduce "neutrabelian algebras", and prove that finite, hereditarily neutrabelian algebras with a cube term are dualizable.