Notes on 8 Majorana Fermions

We discuss a (2+1) dimensional topological superconductor with $N_f$ left- and right-moving Majorana edge modes and a $\mathbb{Z}_2\times \mathbb{Z}_2$ symmetry. In the absence of interactions, these phases are distinguished by an integral topological invariant $N_f$. With interactions, the edge state in the case $N_f=8$ is unstable against interactions, and a $\mathbb{Z}_2\times \mathbb{Z}_2$ invariant mass gap can be generated dynamically. We show that this phenomenon is cl...

In the present letter we indicate an extension of the pure gravity inverse scattering integration technique to the case when fermions (introduced on the base of supersymmetry) are present. In this way the integrability technique for simple ($N=1$) supergravity in two space-time dimensions coupled to the matter fields taking values in the Lie algebra of $E_{8\left( +8\right) }$ group is developed. This theory contains matter living only in one Weyl representation of $SO\left( ...

A bosonic string in twenty six dimensions is effectively reduced to four dimensions by eleven Majorana fermions which are vectors in the bosonic represetation SO(d-1,1). By dividing the fermions in two groups, actions can be written down which are world sheet supersymmetric, 2-d local and local 4-d supersymmetric. The novel string is anomally free, free of ghosts and the partition function is modular invariant.

Recently it has been suggested by A. M. Tsvelik that quantum S=1/2 antiferromagnet can be described by the Majorana fermions in an irreducible way and without any constraint. In contrast to this claim we shall show that this representation is highly reducible. It is a direct sum of four irreducible fundamental representations of $su(2)$ algebra.

We discuss some possible relationships in gauge theories, string theory and M theory in the light of some recent results obtained in gauge invariant supersymmetric quantum mechanics. In particular this reveals a new relationship between the gauge group E_8 and 11-dimensional space.

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 a bosonic theory. But if the gravitational anomaly only vanishes mod 8, then only gauging $(-1)^F$ is allowed, and the result is a fermionic theory. Our goal is to understand in detail how this happens, despite the fact $(-1)^F$ is defined ...

This contribution gives a panoramic overview of the development of N=8 supergravity and its relation to other maximally supersymmetric theories over the past 40 years. It also provides a personal perspective on the future role of this theory in attempts at unification.

We argue that $\mathcal N=8$ supergravity in four dimensions exhibits an exceptional $E_{8(8)}$ symmetry, enhanced from the known $E_{7(7)}$ invariance. Our procedure to demonstrate this involves dimensional reduction of the $\mathcal N=8$ theory to $d=3$, a field redefinition to render the $E_{8(8)}$ invariance manifest, followed by dimensional oxidation back to $d=4$.

We study the symmetry structure of N=8 quantum mechanics, and apply it to the physics of D0-brane probes in type I' string theory. We focus on the theory with a global $Spin(8)$ R symmetry which arises upon dimensional reduction from $2d$ field theory with $(0,8)$ supersymmetry. There are several puzzles involving supersymmetry which we resolve. In particular, by taking into account the gauge constraint and central charge we explain how the system preserves supersymmetry desp...

In the present paper we constructed the supercharges and Hamiltonians for all variants of superconformal mechanics associated with the superalgebras $osp(8|2), F(4), osp(4^*|4)$, and $su(1,1|4)$. The fermionic and bosonic fields involved were arranged into generators spanning $so(8), so(7), so(5) \oplus su(2)$ and $su(4) \oplus u(1)$ $R$-symmetries of the corresponding superconformal algebras. The bosonic and fermionic parts of these $R$-symmetry generators separately define ...