scholarly journals SUSY-breaking scenarios with a mildly violated $$\varvec{R}$$ symmetry

2021 ◽  
Vol 81 (9) ◽  
Author(s):  
Constantinos Pallis
Keyword(s):  
Scalar Curvature ◽  
Order Term ◽  
Higher Order ◽  
Susy Breaking ◽  
Fine Tuning ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Hidden Sector ◽  
Higher Order Term ◽  
R Symmetry

AbstractNew realizations of the gravity-mediated SUSY breaking are presented consistently with an R symmetry. We employ monomial superpotential terms for the hidden-sector (goldstino) superfield and Kähler potentials parameterizing compact or non-compact Kähler manifolds. Their scalar curvature may be systematically related to the R charge of the goldstino so that Minkowski solutions without fine tuning are achieved. A mild violation of the R symmetry by a higher order term in the Kähler potentials allows for phenomenologically acceptable masses for the R axion. In all cases, non-vanishing soft SUSY-breaking parameters are obtained and a solution to the $$\mu $$ μ problem of MSSM may be accommodated by conveniently applying the Giudice–Masiero mechanism.

Derivation of Skyrme Lagrangian and higher-order term

1990 ◽  
Vol 41 (9) ◽  
pp. 2930-2932
Author(s):  
Akihiro Ito
Keyword(s):  
Order Term ◽  
Higher Order ◽  
Higher Order Term

scholarly journals On some compact almost Kähler locally symmetric space

1998 ◽  
Vol 21 (1) ◽  
pp. 69-72 ◽  
Author(s):  
Takashi Oguro
Keyword(s):  
Symmetric Space ◽  
Scalar Curvature ◽  
Kähler Manifold ◽  
Kähler Manifolds ◽  
Kahler Manifolds ◽  
Locally Symmetric Space ◽  
Kahler Manifold ◽  
Almost Kähler

In the framework of studying the integrability of almost Kähler manifolds, we prove that if a compact almost Kähler locally symmetric spaceMis a weakly ,∗-Einstein vnanifold with non-negative ,∗-scalar curvature, thenMis a Kähler manifold.

scholarly journals A rewriting calculus for cyclic higher-order term graphs

2007 ◽  
Vol 17 (3) ◽  
pp. 363-406 ◽  
Author(s):  
PAOLO BALDAN ◽  
CLARA BERTOLISSI ◽  
HORATIU CIRSTEA ◽  
CLAUDE KIRCHNER
Keyword(s):  
Order Term ◽  
Equational Theory ◽  
Term Rewriting ◽  
Higher Order ◽  
Graph Representation ◽  
First Order ◽  
Rewrite Rules ◽  
Evaluation Mechanism ◽  
Matching Constraints ◽  
Higher Order Term

The Rewriting Calculus (ρ-calculus, for short) was introduced at the end of the 1990s and fully integrates term-rewriting and λ-calculus. The rewrite rules, acting as elaborated abstractions, their application and the structured results obtained are first class objects of the calculus. The evaluation mechanism, which is a generalisation of beta-reduction, relies strongly on term matching in various theories.In this paper we propose an extension of the ρ-calculus, called ρg-calculus, that handles structures with cycles and sharing rather than simple terms. This is obtained by using recursion constraints in addition to the standard ρ-calculus matching constraints, which leads to a term-graph representation in an equational style. Like in the ρ-calculus, the transformations are performed by explicit application of rewrite rules as first-class entities. The possibility of expressing sharing and cycles allows one to represent and compute over regular infinite entities.We show that the ρg-calculus, under suitable linearity conditions, is confluent. The proof of this result is quite elaborate, due to the non-termination of the system and the fact that ρg-calculus-terms are considered modulo an equational theory. We also show that the ρg-calculus is expressive enough to simulate first-order (equational) left-linear term-graph rewriting and α-calculus with explicit recursion (modelled using a letrec-like construct).

Asymptotic expansions for laminar forced-convection heat and mass transfer Part 2. Boundary-layer flows

1966 ◽  
Vol 24 (2) ◽  
pp. 339-366 ◽  
Author(s):  
J. D. Goddard ◽  
Andreas Acrivos
Keyword(s):  
Heat Transfer ◽  
Boundary Layer ◽  
Mass Transfer ◽  
Prandtl Number ◽  
Order Term ◽  
Higher Order ◽  
Convection Heat ◽  
Boundary Layer Flows ◽  
Prandtl Numbers ◽  
Higher Order Term

This is the second of two articles by the authors dealing with asymptotic expansions for forced-convection heat or mass transfer to laminar flows. It is shown here how the method of the first paper (Acrivos & Goddard 1965), which was used to derive a higher-order term in the large Péclet number expansion for heat or mass transfer to small Reynolds number flows, can yield equally well higher-order terms in both the large and the small Prandtl number expansions for heat transfer to laminar boundary-layer flows. By means of this method an exact expression for the first-order correction to Lighthill's (1950) asymptotic formula for heat transfer at large Prandtl numbers, as well as an additional higher-order term for the small Prandtl number expansion of Morgan, Pipkin & Warner (1958), are derived. The results thus obtained are applicable to systems with non-isothermal surfaces and arbitrary planar or axisymmetric flow geometries. For the latter geometries a derivation is given of a higher-order term in the Péclet number expansion which arises from the curvature of the thermal layer for small Prandtl numbers. Finally, some applications of the results to ‘similarity’ flows are also presented.

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