Related papers: Commutative/Non-Commutative Dualities
In this paper, we apply the methods developed in recent work for constructing A-twisted (2,2) Landau-Ginzburg models to analogous (0,2) models. In particular, we study (0,2) Landau-Ginzburg models on topologically non-trivial spaces away…
Isomorphisms are constructed between generalized Schur algebras in different degrees. The construction covers both the classical case (of general linear groups over infinite fields of arbitrary characteristic) and the quantized case (in…
A construction is proposed for linear connections on non-commutative algebras. The construction relies on a generalisation of the Leibnitz rules of commutative geometry and uses the bimodule structure of $\Omega^1$. A special role is played…
We discuss the Hodge theory of algebraic non-commutative spaces and analyze how this theory interacts with the Calabi-Yau condition and with mirror symmetry. We develop an abstract theory of non-commutative Hodge structures, investigate…
The Landau problem in the noncommutative plane is discussed in the context of realizations of the two-fold centrally extended planar Galilei group and the anyon theory.
We show that 4D gauge theories with Green-Schwarz anomaly cancellation and possible generalized Chern-Simons terms admit a formulation that is manifestly covariant with respect to electric/magnetic duality transformations. This generalizes…
We discuss continuous duality transformations and the properties of classical theories with invariant interactions between electromagnetic fields and matter. The case of scalar fields is treated in some detail. Special discrete elements of…
In this short letter, we rediscuss the model for non-commutative U(1) gauge theory presented in [arXiv:0912.2634] and argue that by treating the "soft-breaking terms" of that model in the realm of an extended BRST symmetry, a future…
We use the exact renormalization group (ERG) perturbatively to construct the Wilson action for the two-dimensional O(N) non-linear sigma model. The construction amounts to regularization of a non-linear symmetry with a momentum cutoff. A…
We discuss our attempts to generalize the known examples of dualities in N=1 supersymmetric gauge theories to exceptional gauge groups. We derive some dual pairs from known examples connected to exceptional groups and find an interesting…
Going beyond the linearized study has been a longstanding problem in the theory of Landau damping. In this paper we establish exponential Landau damping in analytic regularity. The damping phenomenon is reinterpreted in terms of transfer of…
Taking into account the recent developments associated with duality in physics, this article is focused on investigating the properties of a tensor generalization of the electrodynamics dual to the standard vector model even considering the…
We show that noncommuting electric fields occur naturally in $\theta$-expanded noncommutative gauge theories. Using this noncommutativity, which is field dependent, and a hamiltonian generalisation of the Seiberg-Witten Map, the algebraic…
We discuss scalar quantum field theories in a Lorentz-invariant three-dimensional noncommutative space-time. We first analyze the one-loop diagrams of the two-point functions, and show that the non-planar diagrams are finite and have…
We define a theory of noncommutative general relativity for canonical noncommutative spaces. We find a subclass of general coordinate transformations acting on canonical noncommutative spacetimes to be volume-preserving transformations.…
The three original publications in this thesis encompass various aspects in the still developing area of noncommutative quantum field theory, ranging from fundamental concepts to model building. One of the key features of noncommutative…
We complete the first stage of constructing a theory of fields not investigated before; these fields transform according to Lorentz group representations decomposable into an infinite direct sum of finite-dimensional irreducible…
We discuss non-commutative field theories in coordinate space. To do so we introduce pseudo-localized operators that represent interesting position dependent (gauge invariant) observables. The formalism may be applied to arbitrary field…
A class of two-dimensional globally scale-invariant, but not conformally invariant, theories is obtained. These systems are identified in the process of discussing global and local scaling properties of models related by duality…
The fundamental field equations in modified gravity (including general relativity; massive and bimetric theories; Ho\vrava-Lifshits, HL; Einstein--Finsler gravity extensions etc) posses an important decoupling property with respect to…