Related papers: Three-point non-associative supersymmetry generali…
It is shown that the Hamilton equations in supersymmetric quantum mechanics can be presented in nonassociative form, where the Hamiltonian is decomposed into two nonassociative factors.
Non-associtive algebras is a research direction gaining much attention these days. New developments show that associative algebras and some not-associative structures can be unified at the level of Yang-Baxter structures. In this paper, we…
In this article one extends the classical theory of (intermediate) Jacobians to the "noncommutative world". Concretely, one constructs a Q-linear additive Jacobian functor J(-) from the category of noncommutative Chow motives to the…
The supersymmetric generalization of a recently proposed Abelian axial gauge model with antisymmetric tensor matter fields is presented.
We study asymptotically non-free gauge theories and search for renormalization group invariant (i.e. technically natural) relations among the couplings which lead to successful gauge-Yukawa unification. To be definite, we consider a…
The first class constraints in N = 1 supergravity in 2 + 1 dimensions are used to construct a generator of three gauge symmetries (including a local supersymmetry) that leave the action invariant. The algebra of these symmetries closes.…
In this study we develop a systematic procedure to construct a Poisson operator that describes the dynamics of a three dimensional nonholonomic system. Instead of reducing by symmetry the antisymmetric operator that links the energy…
We derive extremal black hole solutions for a variety of four dimensional models which, after Kaluza-Klein reduction, admit a description in terms of 3D gravity coupled to a sigma model with symmetric target space. The solutions are in…
This paper shows how the forms of gauge theory, Hamiltonian mechanics and quantum mechanics arise from a non-commutative framework for calculus and differential geometry. Discrete calculus is seen to fit into this pattern by reformulating…
We investigate the most general non(anti)commutative geometry in N=1 four-dimensional superspace, invariant under the classical (i.e., undeformed) supertranslation group. We find that a nontrivial non(anti)commutative superspace geometry…
We introduce a notion of Q-algebra that can be considered as a generalization of the notion of Q-manifold (a supermanifold equipped with an odd vector field obeying {Q,Q} =0). We develop the theory of connections on modules over Q-algebras…
The associator of a non-associative algebra is the curvature of the Hochschild quasi-complex. The relationship ``curvature-associator'' is investigated. Based on this generic example, we extend the geometric language of vector fields to a…
We present a method of constructing generic single-centered and multi-centered extremal black hole solutions in a large class of 4D N=2 supergravities coupled to vector-multiplets with cubic prepotentials. The method is applicable to models…
We determine the general coupling of a system of scalars and antisymmetric tensors, with at most two derivatives and undeformed gauge transformations, for both rigid and local N=2 supersymmetry in four-dimensional spacetime. Our results…
We perform Monte Carlo calculation of correlation functions in 4d N=4 super Yang-Mills theory on R*S^3 in the planar limit. In order to circumvent the well-known problem of lattice SUSY, we adopt the idea of a novel large-N reduction, which…
We further develop a noncommutative model unifying quantum mechanics and general relativity proposed in {\it Gen. Rel. Grav.} (2004) {\bf 36}, 111-126. Generalized symmetries of the model are defined by a groupoid $\Gamma $ given by the…
We summarize the emergence of non-commutative/non-associative structures in Dirac's generalization of Maxwell theory, focusing mostly on the magnetic field analogue of the non-geometric R-flux string model. The cohomological interpretation…
Gauge theories are important descriptions for many physical phenomena and systems in quantum computation. Automorphism of gauge group naturally gives global symmetries of gauge theories. In this work we study such symmetries in gauge…
We have analyzed and proposed coupling mechanisms between Three Josephson Junction Flux Qubits (3JJQ). For this, we have developed a numerical method to extract the effective Hamiltonian of a system of coupled qubits via the…
The representations of the observable algebra of a low dimensional quantum field theory form the objects of a braided tensor category. The search for gauge symmetry in the theory amounts to finding an algebra which has the same…