Related papers: Conformal maps in higher dimensions and derived ge…
Higher dimensional Euclidean Liouville conformal field theories (LCFTs) consist of a log-correlated real scalar field with a background charge and an exponential potential. We analyse the LCFT on a four-dimensional manifold with a boundary.…
In this paper we construct certain irreducible infinite dimensional representations of algebraic groups with Frobenius maps. In particular, a few classical results of Steinberg and Deligne & Lusztig on complex representations of finite…
In this note, we use give some algebraic applications of a previous result by the author which compares the deformations parameterized by the Maurer-Cartan elements of a differential graded Lie algebra, and a differential graded Lie…
We study 4-dimensional simply connected Lie groups $G$ with left-invariant Riemannian metric $g$ admitting non-trivial conformal Killing 2-forms. We show that either the real line defined by such a form is invariant under the group action,…
Motivated by the theory of unitary representations of finite dimensional Lie supergroups, we describe those Lie superalgebras which have a faithful finite dimensional unitary representation. We call these Lie superalgebras unitary. This is…
We consider scalar field theory in the D-dimensional space with nontrivial metric and local action functional of most general form. It is possible to construct for this model a generalization of renormalization procedure and RG-equations.…
Conformal transformations of the following kinds are compared: (1) conformal coordinate transformations, (2) conformal transformations of Lagrangian models for a D-dimensional geometry, given by a Riemannian manifold M with metric g of…
We consider the dimensional reduction of a CFT, breaking multiplets of the d-dimensional conformal group SO(d+1,1) up into multiplets of SO(d,1). This leads to an expansion of d-dimensional conformal blocks in terms of blocks in d-1…
We analyze conformal blocks with multiple (semi-)degenerate field insertions in Liouville/Toda conformal field theories an show that their vector space is fully reproduced by the four-dimensional limit of open topological string amplitudes…
We obtain a complete classification of all finite-dimensional irreducible modules over classical map superalgebras, provide formulas for their (super)characters and a description of their extension groups. Furthermore, we describe the block…
In the first part we present the Weyl algebra and our results concerning its finite-dimensional Lie subalgebras. The second part is devoted to a more exotic algebraic structure, the Lie algebra of order 3. We set the basis of a theory of…
We reformulate the Omega-deformation of four-dimensional gauge theory in a way that is valid away from fixed points of the associated group action. We use this reformulation together with the theory of coisotropic A-branes to explain recent…
We present a new supersymmetric integrable model: the $N=2$ superconformal affine Liouville theory. It interpolates between the $N=2$ super Liouville and $N=2$ super sine-Gordon theories and possesses a Lax representation on the complex…
The notions of conformal Lie 2-algebras and conformal omni-Lie algebras are introduced and studied. It is proved that the category of conformal Lie 2-algebras and the category of 2-term conformal $L_{\infty}$-algebras are equivalent. We…
The historical developments of conformal transformations and symmetries are sketched: Their origin from stereographic projections of the globe, their blossoming in two dimensions within the field of analytic complex functions, the generic…
We describe arbitrary multiplicative differential forms on Lie groupoids infinitesimally, i.e., in terms of Lie algebroid data. This description is based on the study of linear differential forms on Lie algebroids and encompasses many known…
We construct a new family of infinite-dimensional quasi-graded Lie algebras on hyperelliptic curves. We show that constructed algebras possess infinite number of invariant functions and admit a decomposition into the direct sum of two…
We reconsider non-degenerate second order superintegrable systems in dimension two as geometric structures on conformal surfaces. This extends a formalism developed by the authors, initially introduced for (pseudo-)Riemannian manifolds of…
Let $R$ be a Lie conformal algebra. The purpose of this paper is to investigate the conformal derivation algebra $CDer(R)$, the conformal quasiderivation algebra $QDer(R)$ and the generalized conformal derivation algebra $GDer(R)$. The…
We present a new framework for a Lagrangian description of conformal field theories in various dimensions based on a local version of d+2-dimensional conformal space. The results include a true gauge theory of conformal gravity in d=(1,3)…