Related papers: Notes on 8 Majorana Fermions
Redefining the vacuum state of a free twofold N=1 covariant supersymmetric string action as the one with all the world sheet fermionic excited states occupied, makes the theory anomaly free in D=4 with Minkowski signature. The theory thus…
In the Majorana representation of a spin 1/2 we find an identity which relates spin-spin correlators to one-particle fermionic correlators. This should be contrasted with the straightforward approach in which two-particle (four-fermion)…
We study quantum multicritical behavior in a (2+1)-dimensional Gross-Neveu-Yukawa field theory with eight-component Dirac fermions coupled to two triplets of order parameters that act as Dirac masses, and transform as $(1,0) + (0,1)$…
Sum rules in effective field theories, predicated upon causality, place restrictions on scattering amplitudes mediated by effective contact interactions. Through unitarity of the $S$-matrix, these imply that the size of higher dimensional…
Working over an arbitrary base scheme, we provide an alternative development of triality which does not use Octonion algebras or symmetric composition algebras. Instead, we use the Clifford algebra of the split hyperbolic quadratic form of…
We study the fermionic sector of a probe D8-brane in the supergravity background made of D4-branes compactified on a circle with supersymmetry broken explicitly by the boundary conditions. At low energies the dual field theory is…
Discrete charge, parity, and time symmetries (C, P, and T) of quantized fermion states are extended by a triality symmetry (t), producing the CPTt Group, transforming between three generations of fermions.
Through a systematic symmetry and topology analysis we establish that three-dimensional chiral superconductors with strong spin-orbit coupling and odd-parity pairing generically host low-energy nodal quasiparticles that are…
For a fermionic quantum field theory in $d=1+1$ dimensions, there is a subtle difference between summing over spin structures and gauging $(-1)^F$. If the gravitational anomaly vanishes mod 16, then both operations are equivalent and yield…
We suggest a simple supersymmetric SO(10) grand unified theory in 6 dimensions which produces the suitable fermion mass hierarchies. The 5th and 6th dimensional coordinates are compactified on a $T^2/Z_2$ orbifold. The gauge and Higgs…
We suggest simple models which produce the suitable fermion mass hierarchies and flavor mixing angles based on the 6 dimensional N=1 supersymmetric SO(10) grand unified theory compactified on a $T^2/(Z_2 \times Z_2')$ orbifold. We introduce…
Based on a few basic assumptions, a predictive supersymmetric grand unification $G_{U}=SO(10)\times \Delta_{48}(SU(3))\times U(1)$ model is proposed. Thus, all the observed 45 chiral fermions with additional 3 right-handed neutrinos are…
Topological phases which host Majorana fermions can not be identified via local order parameters. We give simple nonlocal order parameters to distinguish quasi-one-dimensional (1D) topological superconductors of spinless fermions, for any…
We redo the quantization of the N=4 string, taking into account the reducibility of the constraints. The result is equivalent to the N=2 string, with critical dimension D=4 and signature (++--). The N=4 formulation has several advantages:…
The Weyl fermions with a well defined chirality are known to demand that the dimension of space which they inhabit must be odd. It is shown here, however, that not all odd dimensional spaces are equally good hosts: in particular, an…
We study theoretically the role of topological invariants to protect the Majorana fermions in a model of two-dimensional chiral superconductors which belong to class D of topological periodic table. A rich phase diagram is revealed. Each…
This short article on a thermodynamic signature of Majorana fermions confined on the surface of a 3D topological superfluid in the presence of a moving condensate was circulated to a limited audience in Fall 2013. Since recent experiments…
We suggest simple models which produce the suitable fermion mass hierarchies and flavor mixing angles based on the 6 dimensional N=1 supersymmetric SO(10) grand unified theory compactified on a $T^2/(Z_2 \times Z_2')$ orbifold. We introduce…
We study the generation of Majorana fermions in a two-dimensional topological superconductor placed in a transverse magnetic field B. A topological insulator/superconductor heterostructure and a two-dimensional p-wave superconductor are…
Supersymmetry can be consistently generalized in one and two dimensional spaces, fractional supersymmetry being one of the possible extension. 2D fractional supersymmetry of arbitrary order $F$ is explicitly constructed using an adapted…