A direct road to Majorana fields

A concise discussion of spin-1/2 field equations with a special focus on Majorana spinors is presented. The Majorana formalism which describes massive neutral fermions by the help of two-component or four-component spinors is of fundamental importance for the understanding of mathematical aspects of supersymmetric and other extensions of the Standard Model of particle physics, which may play an increasingly important role at the beginning of the LHC era. The interplay between the two-component and the four-component formalism is highlighted in an introductory way. Majorana particles are predicted both by grand unified theories, in which these particles are neutrinos, and by supersymmetric theories, in which they are photinos, gluinos and other states.Comment: 30 pages, LATEX, one section expanded and references adde

Proximity-induced supercurrent through topological insulator based nanowires for quantum computation studies

Proximity induced superconducting energy gap in the surface states of topological insulators has been predicted to host the much wanted Majorana fermions for fault tolerant quantum computation. Recent theoretically proposed architectures for topological quantum computation via Majoranas are based on large networks of Kitaevs one dimensional quantum wires, which pose a huge experimental challenge in terms of scalability of the current single nanowire based devices. Here, we address this problem by realizing robust superconductivity in junctions of fabricated topological insulator Bi2Se3 nanowires proximity coupled to conventional s wave superconducting W electrodes. Milling technique possesses great potential in fabrication of any desired shapes and structures at nanoscale level, and therefore can be effectively utilized to scale up the existing single nanowire based design into nanowire based network architectures. We demonstrate the dominant role of ballistic topological surface states in propagating the long range proximity induced superconducting order with high IcRN product in long Bi2Se3 junctions. Large upper critical magnetic fields exceeding the Chandrasekhar Clogston limit suggests the existence of robust superconducting order with spin triplet cooper pairing. An unconventional inverse dependence of IcRN product on the width of the nanowire junction was also observed.Comment: 12 page

Superconductivity in a spin liquid - a one dimensional example

We study a one-dimensional model of interacting conduction electrons with a two-fold degenerate band away from half filling. The interaction includes an on-site Coulomb repulsion and Hund's rule coupling. We show that such one-dimensional system has a divergent Cooper pair susceptibility at T = 0, provided the Coulomb interaction $U$ between electrons on the same orbital and the modulus of the Hund's exchange integral $|J|$ are larger than the interorbital Coulomb interaction. It is remarkable that the superconductivity can be achieved for {\it any} sign of $J$. The opening of spectral gaps makes this state stable with respect to direct electron hopping between the orbitals. The scaling dimension of the superconducting order parameter is found to be between 1/4 (small $U$) and 1/2 (large $U$).Comment: 11 pages, Latex, no figure

A locally supersymmetric SO(10,2)SO(10,2) invariant action for D=12D=12 supergravity

We present an action for $N=1$ supergravity in $10+2$ dimensions, containing the gauge fields of the $OSp(1|64)$ superalgebra, i.e. one-forms $B^{(n)}$ with $n$=1,2,5,6,9,10 antisymmetric D=12 Lorentz indices and a Majorana gravitino $\psi$. The vielbein and spin connection correspond to $B^{(1)}$ and $B^{(2)}$ respectively. The action is not gauge invariant under the full $OSp(1|64)$ superalgebra, but only under a subalgebra ${\tilde F}$ (containing the $F$ algebra $OSp(1|32)$), whose gauge fields are $B^{(2)}$, $B^{(6)}$, $B^{(10)}$ and the Weyl projected Majorana gravitino ${1 \over 2} (1+\Gamma_{13}) \psi$. Supersymmetry transformations are therefore generated by a Majorana-Weyl supercharge and, being part of a gauge superalgebra, close off-shell. The action is simply $\int STr ({\bf R}^6 {\bf \Gamma})$ where ${\bf R}$ is the $OSp(1|64)$ curvature supermatrix two-form, and ${\bf \Gamma}$ is a constant supermatrix involving $\Gamma_{13}$ and breaking $OSp(1|64)$ to its ${\tilde F}$ subalgebra. The action includes the usual Einstein-Hilbert term.Comment: LaTeX, 13 pages. Added a reference, a Table in Appendix A for the gamma commutations in d=12, and corrected eq. (4.14) for the Einstein-Hilbert term; v4: corrected formulas (A.3), (A.4) and (A.10), modified last paragraph of Section 5, added acknowledgement

Neutrinos and the matter-antimatter asymmetry in the Universe

The discovery of neutrino oscillations provides a solid evidence for nonzero neutrino masses and leptonic mixing. The fact that neutrino masses are so tiny constitutes a puzzling problem in particle physics. From the theoretical viewpoint, the smallness of neutrino masses can be elegantly explained through the seesaw mechanism. Another challenging issue for particle physics and cosmology is the explanation of the matter-antimatter asymmetry observed in Nature. Among the viable mechanisms, leptogenesis is a simple and well-motivated framework. In this talk we briefly review these aspects, making emphasis on the possibility of linking neutrino physics to the cosmological baryon asymmetry originated from leptogenesis.Comment: 8 pages, 1 table, 1 figure; Based on talk given at the Symposium STARS2011, 1 - 4 May 2011, Havana, Cuba; to be published in the Proceeding