相关论文: Aspects of W_\INFTY Symmetry

Symmetry transformations of the space-time fields of string theory are generated by certain similarity transformations of the stress-tensor of the associated conformal field theories. This observation is complicated by the fact that, as we…

We construct four edge contractions for the affine super Yangian of type $A$. By using these edge contractions, we give a homomorphism from the affine super Yangian of type $A$ to the universal enveloping algebra of the non-rectangular…

Our main interest in this paper is chiefly concerned with the conditions characterizing \textit{orthogonal and symplectic abstract differential geometries}. A detailed account about the sheaf-theoretic version of the \textit{symplectic…

We define and study complex structures and generalizations on spaces consisting of geodesics or harmonic maps that are compatible with the symmetries of these spaces. The main results are about existence and uniqueness of such structures.

We present the nontrivial $W_{1+\infty}$ $n$-algebra and analyze its remarkable properties. We investigate the $W_{1+\infty}$ $n$-algebra in the Landau problem and discuss the realization of the classical $w_{\infty}$ 3-algebra.…

The $w_{1+\infty}$ symmetry algebra appears in the Einstein--Yang--Mills theory, proposed recently by Strominger. In this paper, we derive the supersymmetric $w_{1+\infty}$ symmetry by using the known results on the operator product…

Exceptional field theory (EFT) gives a geometric underpinning of the U-duality symmetries of M-theory. In this talk I give an overview of the surprisingly rich algebraic structures which naturally appear in the context of EFT. This includes…

We study the realization of the (super) conformal topological symmetry in two-dimensional field theories. The mirror automorphism of the topological algebra is represented as a reflection in the space of fields. As a consequence, a double…

We study the convexity of the entropy functional along particular interpolating curves defined on the space of finitely supported probability measures on a graph.

I review, some of the algebraic and geometric structures that underlie the theory of Special Relativity. This includes a discussion of relativity as a symmetry principle, derivations of the Lorentz group, its composition law, its Lie…

We review some aspects of the implementation of spacetime symmetries in noncommutative field theories, emphasizing their origin in string theory and how they may be used to construct theories of gravitation. The geometry of canonical…

After briefly reviewing the methods that allow us to derive consistently new Lie (super)algebras from given ones, we consider enlarged superspaces and superalgebras, their relevance and some possible applications.

This is a follow-up of arXiv:2412.07470 [hep-th]. A simplified version of the SM plus gravity, put forward there, is presented here and some of its aspects delved into. The basic structure consists of two sectors, left and right, with…

The geometric structure of theories with gauge fields of spins two and higher should involve a higher spin generalisation of Riemannian geometry. Such geometries are discussed and the case of $W_\infty$-gravity is analysed in detail. While…

We construct an example of an $A_{\infty}$ algebra structure defined over a finite dimensional graded vector space.

Generalisations of geometry have emerged in various forms in the study of field theory and quantization. This mini-review focuses on the role of higher geometry in three selected physical applications. After motivating and describing some…

We discuss the meaning of geometrical constructions associated to loop quantum gravity states on a graph. In particular, we discuss the "twisted geometries" and derive a simple relation between these and Regge geometries.

We review the results of several of our papers about the procedure of extension of Hamiltonians, allowing the construction of families of superintegrable systems with non-trivial polynomial first integrals (or symmetry operators) of…

The true nature of gravity is a remarkable open problem in Gravitation. Theoretical and observational motivations open the avenue of alternative theories of gravity. One possibility resorts to nonminimal couplings and non-metricity…

Some aspects of the geometry of superembeddings and its application to supersymmetric extended objects are discussed. In particular, the embeddings of (3|16) and (6|16) dimensional superspaces into (11|32) dimensional superspace,…