Extended quantum-mechanical supersymmetry in Majorana nanowires*

Extended supersymmetry (SUSY) with central charges has been one of the most important notions in quantum field theory and string theory since the second string revolution in the 90s and the revolution of quantum field theory by Seiberg and Witten. In spite of its great importance in formal aspects of quantum field theory and string theory, all high energy theorists regard it as a useful tool which is not directly related to reality, because the extended N=2 SUSY does not allow chiral fermions relevant for elementary particles such as quarks and leptons. In high energy phenomenology, only N=1 SUSY and its breaking are considered.

In our recent works[1,2], we provide the first experimentally accessible example of extended SUSY with central charges and partial spontaneous SUSY breaking in condensed matter. Specifically, we describe the realization of a periodic chain of partially-overlapping 0D Majorana modes in 1D Majorana nanowires, by applying periodically and spatially modulated potentials or magnetic fields. This system realizes a 1D Majorana dispersive fermion which we identify with the Nambu-Goldstone mode (Goldstino) of the spontaneously and partially broken SUSY. Notice that the famous Witten's no-go theorem prohibiting partial SUSY breaking can be evaded only by the presence of a central extension in the extended SUSY algebra, and our model indeed includes a central extension. Despite the several proposals to realize SUSY in condensed matter, our proposal gives the first condensed matter realization of an extended SUSY with central extensions.

[1] Marra, Inotani, Nitta, arXiv:2106.09039;

[2] Marra, Inotani, Nitta, arXiv:2106.09047.