Related papers: M-theory and Deformation Quantization
We express the covariant actions of a super p-brane and the corresponding equations of motion, in the flat and curved superspaces, in terms of the Nambu (p+1)-brackets. These brackets make the (p+1)-algebra structure of super p-brane…
Branes and defects in topological Landau-Ginzburg models are described by matrix factorisations. We revisit the problem of deforming them and discuss various deformation methods as well as their relations. We have implemented these…
To each natural deformation quantization on a Poisson manifold M we associate a Poisson morphism from the formal neighborhood of the zero section of the cotangent bundle to M to the formal neighborhood of the diagonal of the product M x M~,…
We express the difference between Poisson bracket and deformed bracket for Kontsevich deformation quantization on any Poisson manifold by means of second derivative of the formality quasi-isomorphism. The counterpart on star products of the…
Matrix theory compactifications on tori have associated Yang-Mills theories on the dual tori with sixteen supercharges. A noncommutative description of these Yang-Mills theories based in deformation quantization theory is provided. We show…
Phase Space is the framework best suited for quantizing superintegrable systems--systems with more conserved quantities than degrees of freedom. In this quantization method, the symmetry algebras of the hamiltonian invariants are preserved…
Using a fully covariant formalism given by Carter for the deformation dynamics of p-branes governed by the Dirac-Nambu-Goto action in a curved background, it is proved that the corresponding Witten's phase space is endowed with a covariant…
In this paper, we generalize the Markov triples in two different directions. One is generalization in direction of using the $q$-deformation of rational number introduced by \cite{MO} in connection with cluster algebras, quantum topology…
Let $\{{\cdot},{\cdot}\}_{\boldsymbol{\mathcal{P}}}$ be a variational Poisson bracket in a field model on an affine bundle $\pi$ over an affine base manifold $M^m$. Denote by $\times$ the commutative associative multiplication in the…
We introduce the notion of a "Souriau bracket" on a prequantum circle bundle $Y$ over a phase space $X$ and explain how a deformation of $Y$ in the direction of this bracket provides a genuine quantization of $X$.
One way of reconciling classical and quantum mechanics is deformation quantization, which involves deforming the commutative algebra of functions on a Poisson manifold to a non-commutative, associative algebra, reminiscent of the space of…
We classify the supersymmetric mass deformations of all the super Yang-Mills quantum mechanics, which are obtained by dimensional reductions of minimal super Yang-Mills in spacetime dimensions: ten, six, four, three and two. The resulting…
Fractional branes added to a large stack of D3-branes at the singularity of a Calabi-Yau cone modify the quiver gauge theory breaking conformal invariance and leading to different kinds of IR behaviors. For toric singularities admitting…
Phase space is a framework ideally suited for quantizing superintegrable systems through the use of deformation methods, as illustrated here by applications to de Sitter and chiral particles. Within this framework, Nambu brackets elegantly…
In this paper we generalize the O(p+1,p+1) solution generating technique (this is a method used to deform Dp-branes by turning on a NS-NS B-field) to M-theory, in order to be able to deform M5-brane supergravity solutions directly in eleven…
Recently M. Kontsevich found a combinatorial formula defining a star-product of deformation quantization for any Poisson manifold. Kontsevich's formula has been reinterpreted physically as quantum correlation functions of a topological…
We introduce a Nambu-Poisson bracket in the geometrical description of the D=11 M5-brane. This procedure allows us, under some assumptions, to eliminate the local degrees of freedom of the antisymmetric field in the M5-brane Hamiltonian and…
We give a new method to prove a formula computing a variant of Caldararu's Mukai pairing \cite{Cal1}. Our method is based on some important results in the area of deformation quantization. In particular, part of the work of Kashiwara and…
We review in elementary, non-technical terms the description of topological B-type of D-branes in terms of boundary Landau-Ginzburg theory, as well as some applications.
In these lecture notes I give an introduction to deformation quantization. The quantization problem is discussed in some detail thereby motivating the notion of star products. Starting from a deformed observable algebra, i.e. the star…