Related papers: Notes on 8 Majorana Fermions
We describe a supersymmetric Grand Unified Theory based on the gauge group $\SU(5)^3$, or $\SO(10)^3$, invariant under the interchange of any~SU(5), or~SO(10), with each family multiplet transforming non trivially under one different…
We discuss a scheme for performing Jordan-Wigner transformation for various lattice fermion systems in two and three dimensions which keeps internal and spatial symmetries manifest. The correspondence between fermionic and bosonic operators…
With an assumption that in the Yang-Mills Lagrangian, a left-handed fermion and a right-handed fermion both expressed as the quaternion makes an octonion, and the gauge field can be treated as self-dual, we calculate the axial current and…
In this paper we study a Clifford algebra generalization of the quaternions and its relationship with braid group representations related to Majorana fermions. The Fibonacci model for topological quantum computing is based on the fusion…
In this work we show the existence of supersymmetry and degeneracy for an arbitrary number of Majorana fermions (even or odd) without to invoke any symmetry of Hamiltonian. Next, we analyze the supersymmetry at finite temperature using the…
We perform a detailed conformal field theory analysis of D2-brane instanton effects in four-dimensional type IIA string vacua with intersecting D6-branes. In particular, we explicitly compute instanton induced fermion two-point couplings…
I perform a complete classification of 2d, quasi-1d and 1d topological superconductors which originate from the suitable combination of inhomogeneous Rashba spin-orbit coupling, magnetism and superconductivity. My analysis reveals…
We investigate the spin-statistics connection in arbitrary dimensions for hermitian spinor or tensor quantum fields with a rotationally invariant bilinear Lagrangian density. We use essentially the same simple method as for space dimension…
We develop an effective continuum description for information scrambling in a chain of randomly interacting Majorana fermions. The approach is based on the semiclassical treatment of the path integral for an effective spin chain that…
We show that the generalised geometry formalism provides a new approach to the description of higher-fermion terms in $\mathcal N=1$ supergravity in ten dimensions, which does not appeal to supercovariantisation or superspace. We find…
We apply the Cartan's supersymmetric model to the electromagnetic and weak interaction of leptons and hadrons, and study dynamics of $\pi^0,\eta,\eta'$ meson and Higgs boson. We adopt the Clifford algebra, express Pauli spinors by…
We study theoretically a one-dimensional dimerized Kitaev superconductor model which belongs to BDI class with time-reversal, particle-hole, and chiral symmetries. There are two sources of the particle-hole symmetry, i.e., the sublattice…
An Euclidean representation of bosonized Majorana fermions, prior to imposing constraints, is derived in three space-time dimensons. The difference with the standard three dimensional Ising system is epmhasized. The mild sign problem, does…
A mechanism to generate realistic fermion mass hierarchies based on supersymmetric gauged $U(1)_F$ symmetry in flat five-dimensional (5D) spacetime is proposed. The fifth dimension is compactified on $S^1/Z_2$ orbifold. The standard model…
We summarize our results concerning the spectrum and mass anomalous dimension of SU(2) gauge theories with various numbers of fermions in the adjoint representation, where each Majorana fermion corresponds effectively to half a Dirac…
We compare, following Pati, global symmetries our topological supersymmetric preon model with the heterotic E_8 x E_8 string theory. We include Pati's supergravity based preon model in this work and compare the preon interactions of his…
We study several cases of IR enhancements of global symmetry in four dimensions. In particular, we consider a sequence of $Spin(n+4)$ supersymmetric gauge theories ($8\geq n\geq 1$) with $n$ vectors and spinor matter with $32$ components.…
A four dimensional Superstring is constructed starting from a twenty six dimensional bosonic string. Fermions are introduced by noting the Manselstam's proof of equivalence of two fermions to one boson in 1+1 dimensions. The action of the…
A 5D SU(7) family unification model with two spinor representations of SO(14) is presented. The fifth dimension is compactified on $S^1/Z_2\times Z_2'$. The orbifolding is used to obtain 4D SO(10) chiral fermions. The 4D grand unification…
This article is a write-up of the talk given in one of the mini-symposia of the 2024 European Congress of Mathematicians. I will explain some basics of the representation theory underlying Spin(10) and SU(5) Grand Unified Theories. I will…