Related papers: An extended fuzzy supersphere and twisted chiral s…
We write down scalar field theory and gauge theory on two-dimensional noncommutative spaces ${\cal M}$ with nonvanishing curvature and non-constant non-commutativity. Usual dynamics results upon taking the limit of ${\cal M}$ going to i) a…
We associate an square to any two dimensional evolution algebra. This geometric object is uniquely determined, does not depend on the basis and describes the structure and the behaviour of the algebra. We determine the identities of degrees…
We consider a reduced model of four-dimensional Yang-Mills theory with a mass term. This matrix model has two classical solutions, two-dimensional fuzzy sphere and two-dimensional fuzzy torus. These classical solutions are constructed by…
We study nonanticommutative deformations of N=2 two-dimensional Euclidean sigma models. We find that these theories are described by simple deformations of Zumino's Lagrangian and the holomorphic superpotential. Geometrically, this…
In the framework of noncommutative geometry we describe spinor fields with nonvanishing winding number on a truncated (fuzzy) sphere. The corresponding field theory actions conserve all basic symmetries of the standard commutative version…
In the presence of an $\Omega$-deformation, local operators generate a chiral algebra in the topological-holomorphic twist of a four-dimensional $\mathcal{N} = 2$ supersymmetric field theory. We show that for a unitary $\mathcal{N} = 2$…
A model is presented that could lead to an interesting extension of the Standard Model. Like a supersymmetric gauge theory, the model is holomorphic and invariant to local superspace gauge transformations. However, the model is not…
Non-Abelian fractional supersymmetry algebra in two dimensions is introduced utilizing $U_q(sl(2,\Rcc))$ at roots of unity. Its representations and the matrix elements are obtained. The dual of it is constructed and the corepresentations…
The Galilean conformal algebra has recently been realised in the study of the non-relativistic limit of the AdS/CFT conjecture. This was obtained by a systematic parametric group contraction of the parent relativistic conformal field…
We discuss some of the key topological aspects of a two $(1+1)$-dimensional (2D) self-interacting non-Abelian gauge theory (having no interaction with matter fields) in the framework of {\it chiral} superfield formalism. We provide the…
We study four dimensional supersymmetric gauge theory on the noncommutative superspace, recently proposed by Seiberg. We construct the gauge-invariant action of N=1 super Yang-Mills theory with chiral and antichiral superfields, which has…
Recently we showed that the spectral flow acting on the N=2 twisted topological theories gives rise to a topological algebra automorphism. Here we point out that the untwisting of that automorphism leads to a spectral flow on the untwisted…
The fuzzy disc is a discretization of the algebra of functions on the two dimensional disc using finite matrices which preserves the action of the rotation group. We define a $\varphi^4$ scalar field theory on it and analyze numerically for…
Noncommutative geometry applied to the standard model of electroweak and strong interactions was shown to produce fuzzy relations among masses and gauge couplings. We refine these relations and show then that they are exhaustive.
We construct the general formulation of N=1 supersymmetric self-dual abelian gauge theory involving auxiliary chiral spinor superfields. Self-duality in this context is just U(N) invariance of the nonlinear interaction of the auxiliary…
We offer a simple non-perturbative formula for the component action of a generic N=1/2 supersymmetric chiral model in terms of an arbitrary number of chiral superfields in four dimensions, which is obtained by the Non-Anti-Commutative (NAC)…
We study chiral algebras in the $\bar{Q}$-cohomology of two dimensional SYK models with extended supersymmetry. In a special limit discovered in arXiv:1805.09325, we are able to construct explicitly a "vertical" single-particle higher-spin…
The finite form of the $N=2$ super-Weyl transformations in the chiral and twisted-chiral irreducible formulations of the two-dimensional $N=2$ superfield supergravity are found in $N=2$ superspace. The super-Weyl anomaly of the $N=2$…
In these proceedings we review the main results concerning superspace geometries with nonanticommutative spinorial variables and field theories formulated on them. In particular, we report on the quantum properties of the WZ model…
A list of superconformal chiral operator product expansion algebras with quadratic nonlinearity in two dimensions is completed on the basis of the known classification of little conformal Lie superalgebras. In addition to the previously…