scholarly journals Magnetic deformation of super-Maxwell theory in supergravity

2020 ◽  
Vol 2020 (8) ◽  
Author(s):  
Ignatios Antoniadis ◽  
Jean-Pierre Derendinger ◽  
Hongliang Jiang ◽  
Gabriele Tartaglino-Mazzucchelli

Abstract A necessary condition for partial breaking of $$ \mathcal{N} $$ N = 2 global supersymmetry is the presence of nonlinear deformations of the field transformations which cannot be generated by background values of auxiliary fields. This work studies the simplest of these deformations which already occurs in $$ \mathcal{N} $$ N = 1 global supersymmetry, and its coupling to supergravity. It can be viewed as an imaginary constant shift of the D-auxiliary real field of an abelian gauge multiplet. We show how this deformation describes the magnetic dual of a Fayet-Iliopoulos term, a result that remains valid in supergravity, using its new-minimal formulation. Local supersymmetry and the deformation induce a positive cosmological constant. Moreover, the deformed U(1) Maxwell theory coupled to supergravity describes upon elimination of the auxiliary fields the gauging of R-symmetry, realised by the Freedman model of 1976. To this end, we construct the chiral spinor multiplet in superconformal tensor calculus by working out explicitly its transformation rules and use it for an alternative description of the new-minimal supergravity coupled to a U(1) multiplet. We also discuss the deformed Maxwell theory in curved superspace.

2016 ◽  
Vol 152 (10) ◽  
pp. 2134-2220 ◽  
Author(s):  
Yichao Tian ◽  
Liang Xiao

Let $F$ be a totally real field in which a prime $p$ is unramified. We define the Goren–Oort stratification of the characteristic-$p$ fiber of a quaternionic Shimura variety of maximal level at $p$. We show that each stratum is a $(\mathbb{P}^{1})^{r}$-bundle over other quaternionic Shimura varieties (for an appropriate integer $r$). As an application, we give a necessary condition for the ampleness of a modular line bundle on a quaternionic Shimura variety in characteristic $p$.


Author(s):  
Natalia Petrovna Golubetskaya

Innovative development of economy is a necessary condition for increase of competitiveness ofRussia. Organization change should pass consistently taking into account a strategic target of development of the Russian economy as a whole. The analysis of work of the large innovatively focused corporations has shown that an important direction of formation of system of innovative activity inRussiais development of interaction, integration of large, small enterprise structures and educational institutions. Stopping development threatens the organization with the stagnation, therefore each organization the plans for development directed on formation of competitive advantages of the organization – strategy are developed. The author analyzes advantages of working out of strategy, the criteria necessary at an estimation of projects within the limits of innovative programs which differ depending on specificity of organizational structure, a skill level of the personnel and efficiency of production as a whole.


2001 ◽  
Vol 16 (34) ◽  
pp. 2221-2230 ◽  
Author(s):  
OLEG V. KECHKIN

A bosonic sector of the four-dimensional low-energy heterotic string theory with two Abelian gauge fields is considered in the stationary case. A new 4× 4 unitary null-curvature matrix representation of the theory is derived and the corresponding formulation based on the use of a new 2 × 2 Ernst type matrix complex potential is developed. The group of hidden symmetries is described and classified in the matrix-valued quasi general relativity form. A subgroup of charge symmetries is constructed and representation which transforms linearly under the action of this symmetry subgroup is established. Also the solution generation procedure based on the application of the total charge symmetry subgroup to the stationary Einstein–Maxwell theory is analyzed.


1989 ◽  
Vol 04 (26) ◽  
pp. 2539-2547 ◽  
Author(s):  
AKIO HOSOYA ◽  
JIRO SODA

We quantize the (1+1)-dimensional Abelian gauge theory on cylinder to illustrate our idea how to extract global modes of topological origin. A new analysis is made for the (2+1)-dimensional Maxwell theory on T2(torus)×R(time). The dynamics is explicitly given for the Wilson loops around cycles of the torus with arbitrary moduli parameters. We also discuss an extension to antisymmetric tensor fields in higher dimensions.


Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 620
Author(s):  
Friedemann Brandt

This article elaborates on an off-shell formulation of D = 4, N = 1 supergravity whose auxiliary fields comprise an antisymmetric tensor field without gauge degrees of freedom. In particular, the relation to new minimal supergravity, a supercovariant tensor calculus and the construction of invariant actions including matter fields are discussed.


2016 ◽  
Vol 4 ◽  
Author(s):  
LASSINA DEMBÉLÉ ◽  
FRED DIAMOND ◽  
DAVID P. ROBERTS

A generalization of Serre’s Conjecture asserts that if $F$ is a totally real field, then certain characteristic $p$ representations of Galois groups over $F$ arise from Hilbert modular forms. Moreover, it predicts the set of weights of such forms in terms of the local behaviour of the Galois representation at primes over $p$. This characterization of the weights, which is formulated using $p$-adic Hodge theory, is known under mild technical hypotheses if $p>2$. In this paper we give, under the assumption that $p$ is unramified in $F$, a conjectural alternative description for the set of weights. Our approach is to use the Artin–Hasse exponential and local class field theory to construct bases for local Galois cohomology spaces in terms of which we identify subspaces that should correspond to ones defined using $p$-adic Hodge theory. The resulting conjecture amounts to an explicit description of wild ramification in reductions of certain crystalline Galois representations. It enables the direct computation of the set of Serre weights of a Galois representation, which we illustrate with numerical examples. A proof of this conjecture has been announced by Calegari, Emerton, Gee and Mavrides.


Author(s):  
Joel Fine ◽  
Yannick Herfray

Conformal geodesics are distinguished curves on a conformal manifold, loosely analogous to geodesics of Riemannian geometry. One definition of them is as solutions to a third-order differential equation determined by the conformal structure. There is an alternative description via the tractor calculus. In this article, we give a third description using ideas from holography. A conformal [Formula: see text]-manifold [Formula: see text] can be seen (formally at least) as the asymptotic boundary of a Poincaré–Einstein [Formula: see text]-manifold [Formula: see text]. We show that any curve [Formula: see text] in [Formula: see text] has a uniquely determined extension to a surface [Formula: see text] in [Formula: see text], which we call the ambient surface of [Formula: see text]. This surface meets the boundary [Formula: see text] in right angles along [Formula: see text] and is singled out by the requirement that it be a critical point of renormalized area. The conformal geometry of [Formula: see text] is encoded in the Riemannian geometry of [Formula: see text]. In particular, [Formula: see text] is a conformal geodesic precisely when [Formula: see text] is asymptotically totally geodesic, i.e. its second fundamental form vanishes to one order higher than expected. We also relate this construction to tractors and the ambient metric construction of Fefferman and Graham. In the [Formula: see text]-dimensional ambient manifold, the ambient surface is a graph over the bundle of scales. The tractor calculus then identifies with the usual tensor calculus along this surface. This gives an alternative compact proof of our holographic characterization of conformal geodesics.


2005 ◽  
Vol 20 (35) ◽  
pp. 2735-2743
Author(s):  
CAYETANO DI BARTOLO ◽  
LORENZO LEAL ◽  
FRANCISCO PEÑA

The equations obeyed by the vacuum expectation value of the Wilson loop of Abelian gauge theories are considered from the point of view of the loop-space. An approximative scheme for studying these loop-equations for lattice Maxwell theory is presented. The approximation leads to a partial difference equation in the area and length variables of the loop, and certain physically motivated ansatz is seen to reproduce the mean field results from a geometrical perspective.


Author(s):  
Andrzej Walicki

It has been widely acknowledged that Vladimir Solov’ëv is the greatest Russian philosopher of the nineteenth century; his significance for Russian philosophy is often compared to the significance of Aleksandr Pushkin for Russian poetry. His first works marked the beginning of the revolt against positivism in Russian thought, followed by a revival of metaphysical idealism and culminating in the so-called Religious-Philosophical Renaissance of the early twentieth century. Unlike the Russian idealists of the Romantic epoch, Solov’ëv was a professional, systematic philosopher. He created the first all-round philosophical system in Russia and thus inaugurated the transition to the construction of systems in Russian philosophical thought. At the same time he remained faithful to the Russian intellectual tradition of reluctance to engage in purely theoretical problems; his ideal of ‘integrality’ postulated that theoretical philosophy be organically linked to religion and social practice. He saw himself not as an academic philosopher, but rather as a prophet, discovering the way to universal regeneration. One of the main themes of Solov’ëv’s philosophy of history was Russia’s mission in universal history. Owing to this he was interested in the ideas of the Slavophiles and, in the first period of his intellectual evolution, established close relations with the Slavophile and Pan-Slavic circle of Ivan Aksakov. He was close also to Dostoevskii, on whom he made a very deep impression. At the beginning of the 1880s he began to dissociate himself from the epigones of Slavophilism; his final break with them came in 1883, when he became a contributor to the liberal and Westernizing Vestnik Evropy (European Messenger). The main reason for this was the pro-Catholic tendency of his thought, which led him to believe that Russia had to acknowledge the primacy of the Pope. In his view, this was a necessary condition of fulfilling Russia’s universal mission, defined as the unification of the Christian Churches and the establishment of a theocratic Kingdom of God on earth. In the early 1890s Solov’ëv abandoned this utopian vision and concentrated on working out an autonomous ethic and a liberal philosophy of law. This reflected his optimistic faith in liberal progress and his confidence that even the secularization of ethics was essentially a part of the divine–human process of salvation. In the last year of his life, however, historiosophical optimism gave way to a pessimistic apocalypticism, as expressed in his philosophical dialogue Tri razgovora (Three Conversations) (1900), and especially the ’Tale of the Antichrist’ appended to it.


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