Related papers: Higher-dimensional Chiral Algebras in the Jouanolo…
We define and study coisotropic structures on morphisms of commutative dg algebras in the context of shifted Poisson geometry, i.e. $P_n$-algebras. Roughly speaking, a coisotropic morphism is given by a $P_{n+1}$-algebra acting on a…
The highest weight modules of the chiral algebra of orthogonal WZW models at level one possess a realization in fermionic representation spaces; the Kac-Moody and Virasoro generators are represented as unbounded limits of even CAR algebras.…
In this article, we study the cohomology of some analytic sheaves on the complementary in the projective space of a suitable infinite collection of hyperplane like the Drinfel'd symetric space. In particular, the sheaf of invertible…
In this article, which builds upon the work done in our previous paper, the chiral aspects of 2dcft on globally hyperbolic Lorentzian manifolds are developed and explored within the perturbative algebraic quantum field theory (pAQFT)…
The Clifford algebra of the endomorphisms of the exterior algebra of a countably dimensional vector space induces natural bosonic shadows, i.e. families of linear maps between the cohomologies of complex grassmannians. The main result of…
We study the holomorphic twist of 3d ${\cal N}=2$ gauge theories in the presence of boundaries, and the algebraic structure of bulk and boundary local operators. In the holomorphic twist, both bulk and boundary local operators form chiral…
Two-dimensional full conformal field theories have been studied in various mathematical frameworks, from algebraic, operator-algebraic to categorical. In this work, we focus our attention on theories with chiral components having pointed…
A covariant twistor action for chiral higher-spin theory in (A)dS and flat space is constructed in terms of a holomorphic Chern-Simons theory on twistor space. The action reproduces all known cubic vertices of chiral higher-spin theory in…
The overlap approach to chiral gauge theories on arbitrary $D$--dimensional lattices is studied. The doubling problem and its relation to chiral anomalies for $D=2$ and 4 is examined. In each case it is shown that the doublers can be…
Guided by the ideas of chirality in the abstract polytope theory, the present paper aims to extend the concept to a more general setting of incidence geometries. The purpose of this paper is to explore the more general framework of thin…
The scalar fields of supersymmetric models are coordinates of a geometric space. We propose a formulation of supersymmetry that is covariant with respect to reparametrizations of this target space. Employing chiral multiplets as an example,…
A geometrical interpretation of the consistent and covariant chiral anomaly is done in the space-time respective Hamiltonian framework.
We review cohomology theories corresponding to the chiral and classical operads. The first one is the cohomology theory of vertex algebras, while the second one is the classical cohomology of Poisson vertex algebras (PVA), and we construct…
It was suggested recently that the study of 1-dimensional QCD with fermions in the adjoint representation could lead to an interesting toy model for strange metals and their holographic formulation. In the high density regime, the infrared…
The residual finite-dimensionality of a $\mathrm{C}^*$-algebra is known to be encoded in a topological property of its space of representations, stating that finite-dimensional representations should be dense therein. We extend this…
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…
Topological interactions will be generated in theories with compact extra dimensions where fermionic chiral zero modes have different localizations. This is the case in many warped extra dimension models where the right-handed top quark is…
We construct relative abelian categories in the sense of MacLane for models of algebraic systems in (co)complete abelian categories. As an example, we consider an analogue of Hochschild-Mitchell cohomology for the functor of Yoneda…
It is typical for a semi-infinite cohomology complex associated with a graded Lie algebra to occur as a vertex operator (or chiral) superalgebra where all the standard operators of cohomology theory, in particular the differential, are…
We consider the class of profinite diffeological spaces, that is, diffeological spaces which diffeologies are deduced by pull-back of diffeologies on finite-dimensional manifolds through a system of projection mappings. This class includes…