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Related papers: Holomorphic Poisson Field Theories

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We propose that general D-dimensional quantum field theories are dual to (D+1)-dimensional local quantum theories which in general include objects with spin two or higher. Using a general prescription, we construct a (D+1)-dimensional…

High Energy Physics - Theory · Physics 2010-04-23 Sung-Sik Lee

In this paper, we first recall the notion of (noncommutative) Poisson conformal algebras and describe some constructions of them. Then we study the formal distribution (noncommutative) Poisson algebras and coefficient (noncommutative)…

Quantum Algebra · Mathematics 2022-09-27 Jiefeng Liu , Hongyu Zhou

We show that if a generator of a differential Gerstenhaber algebra satisfies certain Cartan-type identities, then the corresponding Lie bracket is formal. Geometric examples include the shifted de Rham complex of a Poisson manifold and the…

Quantum Algebra · Mathematics 2013-11-11 Domenico Fiorenza , Marco Manetti

We study a formulation of the standard Poisson sigma model in which the target space Poisson manifold carries the Hamilton action of some finite dimensional Lie algebra. We show that the structure of the action and the properties of the…

Mathematical Physics · Physics 2009-11-07 Roberto Zucchini

The most general gauge-invariant marginal deformation of four-dimensional abelian BF-type topological field theory is studied. It is shown that the deformed quantum field theory is topological and that its observables compute, in addition…

High Energy Physics - Theory · Physics 2011-07-21 Richard J. Szabo

In this paper, we give a description of holomorphic multi-vector fields on smooth compact toric varieties, which generalizes Demazure's result of holomorphic vector fields on toric varieties. Based on the result, we compute the Poisson…

Algebraic Geometry · Mathematics 2019-11-13 Wei Hong

We develop an approach to construct Poisson algebras for non-linear scalar field theories that is based on the Cahiers topos model for synthetic differential geometry. In this framework the solution space of the field equation carries a…

Mathematical Physics · Physics 2017-03-28 Marco Benini , Alexander Schenkel

Consistent Hamiltonian interactions that can be added to an abelian free BF-type class of theories in any n greater or equal to 4 spacetime dimensions are constructed in the framework of the Hamiltonian BRST deformation based on…

High Energy Physics - Theory · Physics 2014-11-18 C. Bizdadea , C. C. Ciobirca , E. M. Cioroianu , S. O. Saliu , S. C. Sararu

A holomorphic Poisson structure induces a deformation of the complex structure as Hitchin's generalized geometry. Its associated cohomology naturally appears as the limit of a spectral sequence of a double complex. The first sheet of this…

Differential Geometry · Mathematics 2014-08-05 Zhuo Chen , Daniele Grandini , Yat-Sun Poon

We discuss an embedding of a vector field for the nonholonomic Routh sphere into a subgroup of commuting Hamiltonian vector fields on six dimensional phase space. The corresponding Poisson brackets are reduced to the canonical Poisson…

Exactly Solvable and Integrable Systems · Physics 2018-03-06 I. A. Bizyaev , A. V. Tsiganov

We classify real Poisson structures on complex toric manifolds of type $(1,1)$ and initiate an investigation of their Poisson cohomology. For smooth toric varieties, such structures are necessarily algebraic and are homogeneous quadratic in…

Differential Geometry · Mathematics 2017-04-07 Arlo Caine , Berit Nilsen Givens

We describe an algebraic approach to the time-dependent noncommutative geometry of a six-dimensional Cahen-Wallach pp-wave string background supported by a constant Neveu-Schwarz flux, and develop a general formalism to construct and…

High Energy Physics - Theory · Physics 2009-11-11 Sam Halliday , Richard J. Szabo

To understand what does Chern-Simons with compact Lie group(does not like Dijkgraaf-Witten model with finite group in 3d) attach to a point, we first give a construction of Topological Quantum Field Theory(TQFT) via Chern-Simons theory in…

Mathematical Physics · Physics 2011-12-05 Yifan Zhang , Ke Wu

Let R be a commutative ring, and let A be a Poisson algebra over R. We construct an (R,A)-Lie algebra structure, in the sense of Rinehart, on the A-module of K\"ahler differentials of A depending naturally on A and the Poisson bracket. This…

Differential Geometry · Mathematics 2013-03-19 Johannes Huebschmann

We construct the commutative Poisson algebra of classical Hamiltonians in field theory. We pose the problem of quantization of this Poisson algebra. We also make some interesting computations in the known quadratic part of the quantum…

Mathematical Physics · Physics 2010-10-21 A. Stoyanovsky

For any type of fundamental groupoid scheme, we construct an algebraic cohomology theory for varieties with coefficients in the base field. This is a minor variant of \'etale cohomology, involving neither de Rham complexes nor…

Algebraic Geometry · Mathematics 2026-02-16 Hyuk Jun Kweon

The subject for investigation in this note is concerned with holomorphic Poisson structures on nilmanifolds with abelian complex structures. As a basic fact, we establish that on such manifolds, the Dolbeault cohomology with coefficients in…

Differential Geometry · Mathematics 2016-01-11 Zhuo Chen , Anna Fino , Yat-Sun Poon

We develop a structure theory for transposed Poisson algebras over fields of characteristic different from two. In particular, we prove that every finite-dimensional transposed Poisson algebra over an algebraically closed field decomposes…

Rings and Algebras · Mathematics 2026-04-30 Amir Fernández Ouaridi

We consider nonholonomic systems which symmetry groups consist of two subgroups one of which represents rotations about the axis of symmetry. After nonholonomic reduction by another subgroup the corresponding vector fields on partially…

Exactly Solvable and Integrable Systems · Physics 2018-03-06 A V Tsiganov

Quantum field theories on noncommutative Minkowski space are studied in a model-independent setting by treating the noncommutativity as a deformation of quantum field theories on commutative space. Starting from an arbitrary Wightman…

Mathematical Physics · Physics 2011-04-14 Harald Grosse , Gandalf Lechner