Majorana representations of the symmetric group of degree 4

AbstractThe Monster group M acts on a real vector space VM of dimension 196,884 which is the sum of a trivial 1-dimensional module and a minimal faithful M-module. There is an M-invariant scalar product (,) on VM, an M-invariant bilinear commutative non-associative algebra product ⋅ on VM (commonly known as the Conway–Griess–Norton algebra), and a subset A of VM∖{0} indexed by the 2A-involutions in M. Certain properties of the quintetM=(M,VM,A,(,),⋅) have been axiomatized in Chapter 8 of Ivanov (2009) [Iv09] under the name of Majorana representation of M. The axiomatization enables one to study Majorana representations of an arbitrary group G (generated by its involutions). A representation might or might not exist, but it always exists whenever G is a subgroup in M generated by the 2A-involutions contained in G. We say that thus obtained representation is based on an embedding of G in the Monster. The essential motivation for introducing the Majorana terminology was the most remarkable result by S. Sakuma (2007) [Sak07] which gave a classification of the Majorana representations of the dihedral groups. There are nine such representations and every single one is based on an embedding in the Monster of the relevant dihedral group. It is a fundamental property of the Monster that its 2A-involutions form a class of 6-transpositions and that there are precisely nine M-orbits on the pairs of 2A-involutions (and also on the set of 2A-generated dihedral subgroups in M). In the present paper we are making a further step in building up the Majorana theory by classifying the Majorana representations of the symmetric group S4 of degree 4. We prove that S4 possesses precisely four Majorana representations. The Monster is known to contain four classes of 2A-generated S4-subgroups, so each of the four representations is based on an embedding of S4 in the Monster. The classification of 2A-generated S4-subgroups in the Monster relies on calculations with the character table of the Monster. Our elementary treatment shows that there are (at most) four isomorphism types of subalgebras in the Conway–Griess-Norton algebra of the Monster generated by six Majorana axial vectors canonically indexed by the transpositions of S4. Two of these subalgebras are 13-dimensional, the other two have dimensions 9 and 6. These dimensions, not to mention the isomorphism type of the subalgebras, were not known before

Constrained Superfields and Standard Realization of Nonlinear Supersymmetry

A constrained superfield formalism has been proposed recently to analyze the low energy physics related to Goldstinos. We prove that this formalism can be reformulated in the language of standard realization of nonlinear supersymmetry. New relations have been uncovered in the standard realization of nonlinear supersymmetry.Comment: 8+1 pages, Latex, expanded discussions on scalar and vector field

Nonlinear Realization of Spontaneously Broken N=1 Supersymmetry Revisited

This paper revisits the nonlinear realization of spontaneously broken N=1 supersymmetry. It is shown that the constrained superfield formalism can be reinterpreted in the language of standard realization of nonlinear supersymmetry via a new and simpler route. Explicit formulas of actions are presented for general renormalizable theories with or without gauge interactions. The nonlinear Wess-Zumino gauge is discussed and relations are pointed out for different definitions of gauge fields. In addition, a general procedure is provided to deal with theories of arbitrary Kahler potentials.Comment: 1+18 pages, LaTe

On the S-wave piD-scattering length in the relativistic field theory model of the deuteron

The S-wave scattering length of the strong pion-deuteron (pi D) scattering is calculated in the relativistic field theory model of the deuteron suggested in [1,2].The theoretical result agrees well with the experimental data. The important role of the Delta-resonance contribution to the elastic pi D-scattering is confirmed.Comment: 7 pages, no figures, accepted for publication in Z. Phys.

Shear-induced chemical segregation in a Fe-based bulk metallic glass at room temperature.

Shear-induced segregation, by particle size, is known in the flow of colloids and granular media, but is unexpected at the atomic level in the deformation of solid materials, especially at room temperature. In nanoscale wear tests of an Fe-based bulk metallic glass at room temperature, without significant surface heating, we find that intense shear localization under a scanned indenter tip can induce strong segregation of a dilute large-atom solute (Y) to planar regions that then crystallize as a Y-rich solid solution. There is stiffening of the material, and the underlying chemical and structural effects are characterized by transmission electron microscopy. The key influence of the soft Fe-Y interatomic interaction is investigated by ab-initio calculation. The driving force for the induced segregation, and its mechanisms, are considered by comparison with effects in other sheared media

Generalized N = 2 Super Landau Models

We generalize previous results for the superplane Landau model to exhibit an explicit worldline N = 2 supersymmetry for an arbitrary magnetic field on any two-dimensional manifold. Starting from an off-shell N = 2 superfield formalism, we discuss the quantization procedure in the general case characterized by two independent potentials on the manifold and show that the relevant Hamiltonians are factorizable. In the restricted case when both the Gauss curvature and the magnetic field are constant over the manifold and, as a consequence, the underlying potentials are related, the Hamiltonians admit infinite series of factorization chains implying the integrability of the associated systems. We explicitly determine the spectrum and eigenvectors for the particular model with CP^1 as the bosonic manifold.Comment: 26 page

Phase separation process preventing thermal embrittlement of a Zr-Cu-Fe-Al bulk metallic glass

The structural changes and mechanical properties of a Zr 63 Cu 22 Fe 5 Al 10 bulk metallic glass (BMG), and a Zr 63 Cu 27 Al 10 one made for comparison, were studied on annealing below the crystallization temperature. The phase composition of the samples was studied by conventional X-ray diffractometry and high-resolution transmission electron microscopy including the atomic-scale elemental mapping. The samples were mechanically tested in compression. The Zr 63 Cu 22 Fe 5 Al 10 bulk metallic glass shows a high strength and good deformability at room temperature both in the as-cast state and after prolonged structural relaxation below the crystallization temperature. The reasons for such behavior are discussed in the present work

A Bound on the Superpotential

We prove a general bound on the superpotential in theories with broken supersymmetry and broken R-symmetry, 2|W|< f_a F, where f_a and F are the R-axion and Goldstino decay constants, respectively. The bound holds for weakly coupled as well as strongly coupled theories, thereby providing an exact result in theories with broken supersymmetry. We briefly discuss several possible applications.Comment: 20 page

Obstetric opinions regarding the method of delivery in women that have had surgery for retinal detachment

OBJECTIVES: We sought to determine international obstetric opinions regarding the influence of a history of rhegmatogenous retinal detachment on the management of labour and to review the evidence base. DESIGN: A questionnaire containing closed questions, with pre-coded response opinions, was designed to obtain a cross-section of the obstetric opinions. SETTING: Questionnaires were distributed at the 20th European Congress of Obstetrics and Gynaecology in Lisbon, Portugal. PARTICIPANTS: One hundred questionnaires were distributed among obstetricians attending the congress and 74 agreed to participate. MAIN OUTCOME MEASURES: Participants were asked to state their preferred method of delivery in such patients and the reasons for their recommendation. Furthermore, we questioned whether there was any difference in opinions depending on generation. RESULTS: The majority of respondents (76%) would recommend assisted delivery (either Caesarean section or instrumental delivery), whereas the remaining 24% would advise normal delivery. Generation is not a factor influencing this decision. The majority (58%) based their decision to alter the management of labour on their personal opinion of standard of care. CONCLUSION: The literature shows that there is little evidence to support the belief that previous retinal surgery increases the risk of re-detachment of the retina during spontaneous vaginal delivery. This short survey shows that the majority of an international sample of obstetricians questioned does not share this viewpoint. Therefore, unnecessary interventions may be occurring in otherwise fit women with a history of retinal detachment

High-resolution transmission electron microscopy investigation of diffusion in metallic glass multilayer films

Lack of plasticity is one of the main disadvantages of metallic glasses. One of the solutions to this problem can be composite materials. Diffusion bonding is promising for composite fabrication. In the present work the diffusion process in glassy multilayer films was investigated. A combination of advanced transmission electron microscopy (TEM)methods and precision sputtering techniques allows visualization and study of diffusion in amorphous metallic layers with high resolution. Multilayered films were obtained by radio frequency sputter deposition of Zr-Cu and Zr-Pd. The multilayers were annealed under a high vacuum (10 −5 Pa)for 1 and 5 h at 400 °C, that is, well below the crystallization temperatures but very close to the glass-transition temperatures of both types of the glassy layer. The structural evolution in the deposited films was investigated by high-resolution transmission electron microscopy. It was observed that, despite the big differences in the atomic mass and size, Pd and Cu have similar diffusion coefficients. Surprisingly, 1 h of annealing results in formation of metastable copper nanocrystals in the Zr-Cu layers which, however, disappear after 5 h of annealing. This effect may be connected with nanovoid formation under a complex stress state evolving upon annealing, and is related to the exceptionally slow relaxation of the glassy layers sealed with a Ta overlayer.The authors acknowledge the financial support through the European Research Council under the ERC Advanced Grants INTELHYB (grant ERC-2013-ADG-340025) and ExtendGlass (grant ERC-2015-AdG-695487), the German Science Foundation (DFG) under the grant SO 1518/1-1, and the Ministry of Education and Science of the Russian Federation in the framework of the ‘Increase Competitiveness’ program of NUST ‘MISiS’ (№ К2-2014-013 and К2-2017-089)