Related papers: Z_2-Graded Cocycles in Higher Dimensions
The self-duality equations for gauge fields in pseudoeuclidean spaces of eight and seven dimensions are considered. Some new classes of solutions of the equations are found.
In two dimensions a large class of gravitational systems including, e.g., $R^2$-gravity can be quantized exactly also when coupled dynamically to a Yang-Mills theory. Some previous considerations on the quantization of pure gravity theories…
It is shown that the ${\cal N}=1$ supersymmetric quantum mechanics (SQM) can be extended to a $\mathbb{Z}_2^n$-graded superalgebra. This is done by presenting quantum mechanical models which realize, with the aid of Clifford gamma matrices,…
The problem of fermions in 1+1 dimensions in the presence of a pseudoscalar Coulomb potential plus a mixing of vector and scalar Coulomb potentials which have equal or opposite signs is investigated. We explore all the possible signs of the…
In generalized Yang-Mills theories scalar fields can be gauged just as vector fields in a usual Yang-Mills theory, albeit it is done in the spinorial representation. The presentation of these theories is aesthetic in the following sense: A…
We study the cohomology of the Schwinger term arising in second quantization of the class of observables belonging to the restricted general linear algebra. We prove that, for all pseudodifferential operators in 3+1 dimensions of this type,…
The Schwinger-Dyson equations in the ladder approximation for $2D$ induced gravity coupled to fermions on a flat background are obtained in conformal gauge. A numerical study of these equations shows the possiblity of chiral symmetry…
The dymamical chiral symmetry breaking in higher- derivative quantum gravity has been investigated on the flat background. The Schwinger- Dyson equations numerical solutions have been found in the ladder approximation. Both two- and four-…
We evaluate the gravitational Schwinger terms for the specific two-dimensional model of Weyl fermions in a gravitational background field using a technique introduced by Kallen and find a relation which connects the Schwinger terms with the…
A superfield formalism for the minimal $\mathbb{Z}_2^2$-graded version of supersymmetry is developed. This is done by using the recently introduced definition of integration on the minimal $\mathbb{Z}_2^2$-superspace. It is shown that one…
The notions of Zinbiel 2-algebras and 2-term $Z_{\infty}$-algebras are introduced. It is proved that the category of Zinbiel 2-algebras and the category of $2$-term $Z_{\infty}$-algebras are equivalent to each other. Crossed module…
Considering a class of (2,0)-super-Yang-Mills multiplets that accommodate a pair of independent gauge potentials in connection with a single symmetry group, we present here their coupling to ordinary matter and to non-linear $\sigma$-models…
We study the classical geometry associated to fractional D3-branes of type IIB string theory on R^4/Z_2 which provide the gravitational dual for N=2 super Yang-Mills theory in four dimensions. As one can expect from the lack of conformal…
We propose the bosonization of a many-body fermion theory in D spatial dimensions through a noncommutative field theory on a (2D-1)-dimensional space. This theory leads to a chiral current algebra over the noncommutative space and…
We discuss a new approach for putting gauge theories on the lattice. The gauge fields are defined on the lattice only, but are interpolated to the interior of the lattice cells, where they couple to continuum fermions. The purpose of this…
We derive the $N=2$ and $4$ super Yang-Mills theories from the viewpoint of the $M_4\times Z_2\times Z_2$ gauge theory. Scalars and pseudoscalars appearing in the theories are regarded as gauge fields along the directions on $Z_2\times Z_2$…
We generalize the real and chiral $ {\cal N} =2 $ super Schr\"odinger algebras to ${\mathbb Z}_2 \times {\mathbb Z}_2$-graded Lie superalgebras. This is done by $D$-module presentation and as a consequence, the $D$-module presentations of…
In this work we use constructs from the dual space of the semi-direct product of the Virasoro algebra and the affine Lie algebra of a circle to write a theory of gravitation which is a natural analogue of Yang-Mills theory. The theory…
Any four-dimensional $\mathcal{N} \geqslant 2$ superconformal field theory possess a protected subsector isomorphic to a two-dimensional chiral algebra \cite{Beem:2013sza}. The goal of these lectures is to provide an introduction to the…
In the present discussion, we have studied the Z2-grading of quaternion algebra (H). We have made an attempt to extend the quaternion Lie algebra to the graded Lie algebra by using the matrix representations of quaternion units. The…