Related papers: Quadratic Duality for Chiral Algebras
We study Cartan-Subalgebras of Lie-Algebras associated to associative algebras.
Let $\{P_1, P_2, P_3, P_4\}$ be a quadruplet of points in $S^3$ . We define a ``dual'' quadruplet of it in a conformal geometric way. We show that the dual of a dual quadruplet coincides with the original one. We also show that the cross…
We study the generalization of $R\to 1/R$ duality to arbitrary conformally invariant sigma models with an isometry. We show that any pair of dual sigma models can be represented as quotients of a self-dual sigma model obtained by gauging…
We consider deformations of the differential of a $q$-differential graded algebra. We prove that it is controlled by a generalized Maurer-Cartan equation. We find explicit formulae for the coefficients $c_k$ involved in that equation.
A general way of interpreting odd dimensional models as a doublet of chiral models is discussed. Based on the equations of motion this dual composition is illustrated. Examples from quantum mechanics, field theory and gravity are…
In this paper, we study a class of Leibniz conformal algebras called quadratic Leibniz conformal algebras. An equivalent characterization of a Leibniz conformal algebra $R=\mathbb{C}[\partial]V$ through three algebraic operations on $V$ are…
The notion of geometrical duality is discussed in the context of both Brans-Dicke theory and general relativity. It is shown that, in some particular solutions, the spacetime singularities that arise in usual Riemannian general relativity…
A formulation of abelian and non-abelian chiral gauge theories is presented together with arguments for the unitarity and renormalisability in four dimensions. IASSNS-HEP-94/70, UM-P-94/96, and RCHEP-94/26.
We survey some algebraic geometric aspects of mirror symmetry and duality in string theory. Some applications of computer algebra to algebraic geometry and string theory are shortly reviewed.
We show that a broad class of three-dimensional $\mathcal{N}=2$ chiral Chern-Simons gauge theories admit an abelian and planar dual description. These chiral-planar dualities emerge by performing real mass deformations on known…
We give a physicist oriented survey of Poisson-Lie symmetries of classical systems. We consider finite dimensional geometric actions and the chiral WZNW model as examples for the general construction. An essential point is that quadratic…
Chiral-parity (parity-doublet) effective Lagrangian models provide a compact and symmetry-consistent framework for describing baryons and their negative-parity partners in terms of linearly-realized chiral symmetry. Unlike the conventional,…
Quadratic algebras are generalizations of Lie algebras; they include the symmetry algebras of 2nd order superintegrable systems in 2 dimensions as special cases. The superintegrable systems are exactly solvable physical systems in classical…
The brief history for the prediction of the nuclear chirality is provided. The theoretical and experimental investigations of the nuclear chirality are reviewed, including the verification of chiral doublet bands, the chiral conundrum and…
In this article we associate a combinatorial differential graded algebra to a cubic planar graph G. This algebra is defined combinatorially by counting binary sequences, which we introduce, and several explicit computations are provided. In…
We employ the Dirac-like equation for the gauge field proposed by Majorana to obtain an action that is symmetric under duality transformation. We also use the equivalence between duality and chiral symmetry in this fermion-like formulation…
In four spacetime dimensions, the classically integrable self-dual sectors of gauge theory and gravity have associated chiral algebras, which emerge naturally from their description in twistor space. We show that there are similar chiral…
In this note, we discuss some properties of the quiver BPS algebras. We consider how they would transform under different operations on the toric quivers, such as dualities and higgsing. We also give free field realizations of the algebras,…
To any graph and smooth algebraic curve $C$ one may associate a "hypercurve" arrangement and one can study the rational homotopy theory of the complement $X$. In the rational case ($C=\mathbb{C}$), there is considerable literature on the…
We introduce a new class of quasi-hereditary algebras, containing in particular the Auslander-Dlab-Ringel (ADR) algebras. We show that this new class of algebras is preserved under Ringel duality, which determines in particular explicitly…