We develop the Palatini formalism within framework of generalized Riemannian geometry Courant algebroids. In this context, variation a Einstein–Hilbert–Palatini action - formed using metric, algebroid connection (in contrary to ordinary case, not necessarily torsionless one) and volume form leads naturally proper notion Levi-Civita low-energy effective actions string theory.

Twisted geometry is a piecewise-flat geometry less rigid than Regge geometry. In Loop Gravity, it provides the classical limit for each step of the truncation utilized in the definition of the quantum theory. We define the torsionless spin-connection of a twisted geometry. The difficulty given by the discontinuity of the triad is addressed by interpolating between triads. The curvature of the r...

Extending a recently proposed procedure of construction of various elements of differential geometry on noncommutative algebras, we obtain these structures on noncommu-tative superalgebras. As an example, a quantum superspace covariant under the action of super-Jordanian OSp h (2/1) is studied. It is shown that there exist a two-parameter family of torsionless connections, and the curvature com...

Effects of gravitational interaction are generally neglected in particle physics. A first order formulation gravity is presented to include Quantum Mechanical Lagrangian fermions. It seen that fermions minimally coupled gives rise a torsionless effective theory with quartic interaction. After passing through thermal background the most generic form contortion contributes neutrino mass. This mas...

Two dimensional gravity with torsion is proved to be equivalent to special types of generalized 2d dilaton gravity. E.g. in one version, the dilaton field is shown to be expressible by the extra scalar curvature, constructed for an independent Lorentz connection corresponding to a nontrivial torsion. Elimination of that dilaton field yields an equivalent torsionless theory, nonpolynomial in cur...

Let be a ring. We use mod (resp. mod ) to denote the category of finitely generated left -modules (resp. right -modules). We always assume that and are Artinian algebras and is a faithfully balanced self-orthogonal bimodule, that is, satisfies the following conditions: (1) is in mod and is in mod ; (2) the natural maps → End op and → End are isomorphisms; (3) Ext = 0 and Ext = 0 for any i ≥ 1. ...

We analyse with the algebraic, regularisation independent, cohomological B.R.S. methods, the renormalisability of torsionless N=2 supersymmetric non-linear σ models built on Kähler spaces. Surprisingly enough with respect to the common wisdom, we obtain an anomaly candidate, at least in the compact Ricci-flat case. In the compact homogeneous Kähler case, as expected, the anomaly candidate disap...

We consider the Quartic Horndeski theory with torsion on a Friedmann-Lema\^{\i}tre-Robertson-Walker background in second-order formalism. show that there is one parameter family of Cartan Lagrangians and all such theories only modify dispersion relations graviton scalar perturbation are usually found standard torsionless spacetime. In other words, for this class, does not induce new degrees fre...

Given a tame differential calculus over noncommutative algebra [Formula: see text] and an text]-bilinear metric consider the conformal deformation being invertible element of We prove that there exists unique connection on bimodule one-forms which is torsionless compatible with derive concrete formula connecting Levi-Civita for As application, we compute Ricci scalar curvatures general perturba...

Let R be a left coherent ring, S a right coherent ring and RU a generalized tilting module, with S = End(RU ) satisfying the condition that each finitely presented left R-module X with ExtR(X,U )= 0 for any i ≥ 1 is U -torsionless. If M is a finitely presented left R-module such that ExtR(M,U )= 0 for any i ≥ 0 with i 6= n (where n is a nonnegative integer), then ExtS(Ext n R(M,U ),U ) ∼= M and...