Supersymmetry and Mirror Symmetry

Nature’s supersymmetry (SUSY) is not what most physicists have thought about. It is not making a copy of all existing particles and giving these superparticles some fancy names like something-ino or s-otherthing.

The big mistake on SUSY has been to confuse some properties of SUSY with those of mirror symmetry which has not drawn deserved attention from the physics community. It is actually the mirror symmetry that makes a mirrored copy of particles in our known sector.

SUSY is more about the balance of degrees of freedom between fermions and bosons. That is, it is a symmetry between matter building block fermions (spin=1/2) and force carrier gauge bosons (spin=1). It is a symmetry that have already sort of been presented in its pseudo form in the Standard Model of particle physics.

Before the mirror symmetry is spontaneously broken, SUSY is perfectly preserved. All particles (matter fermions and gauge bosons) are massless. This makes that each boson has two degrees of freedom from its spin (+1 and -1 just like a photon as zero is not possible for massless bosons), which is the same for a fermion (+1/2 and -1/2). Therefore, the unbroken SUSY can also be regarded as number of bosons = number of fermions. Here anti-fermions are counted as different fermions since they are Dirac particles.

Mirror symmetry is originated from the intrinsic and topologically non-trivial properties of 4-d spacetime where matter fermions (or Dirac spinors, spin=1/2) reside. It is some kind of super-chirality (left and right handed symmetry) for two distinct sectors of particles. When it breaks down, the left-right symmetry is broken, SUSY breaks, and parity & CP symmetries break, even within our own sector. In the end, all left-handed neutrinos are in our normal world while the right-handed neutrinos stay in the mirror world. As such, the weak interaction in our sector is left-handed only. This is also why neutrinos have so tiny masses and why observed current dark energy density is so low.

SUSY serves more like a selection rule for gauge group given a set of fermions. For example, for the three generations of fermions of our world, the only sensible and SUSY-obeying gauge group is Uf(6)xSUc(3)xSUw(2)xUY(1).

More details can be seen in my recent paper “Dark energy and spontaneous mirror symmetry breaking”.

Author: Wanpeng Tan

As a research professor at Notre Dame, I share my ideas and thoughts mainly about mirror matter theory and open science on this blog. Under the new theory, we live in the universe with a mirror (hidden) sector of particles. A perfectly imperfect (minimally broken) mirror symmetry is the key to unlock the beauty and elegance of our universe. Click on the menu links for a popular introduction, a technical summary, and list of my papers on the new mirror matter theory.