4.2 Origins & Connections

summary

One of the biggest ideas in particle physics and condensed matter is symmetry breaking.

The idea of the Higgs mechanism doesn’t only come from studying particles—in fact, in tandem it came from notions about materials.
Materials are easier to study in some ways, since we can adjust their temperature, pressure, etc. on a macro scale and observe results.
The idea of symmetry breaking was one that emerges from properties of certain kinds of materials. When applied to the world of particle physics, symmetry breaking provides a deep understanding of particles and their interactions.
Consider a little man living inside a ferromagnet, the famous example by Sidney Coleman. This man would have a hard time detecting the rotational invariance of the laws of nature; any experiment he attempted would be corrupted by the background magnetic field. And yet, we are aware of the rotational invariance of physics outside this small magnet.

For a long time, physicists believed that nature was characterized by different symmetries.

In a sort of “mirror” world, symmetry would indicate that the physical laws of the universe are the same if “right” and “left” are switched, and matter becomes antimatter.
However, symmetries had been shown to occasionally be “violated” or broken.
Materials can show evidence of spontaneous symmetry breaking. For instance, consider the Curie temperature $T_c$. Magnetic moments are permanent dipole moments within an atom, sourced by electrons’ angular momentum and spin. The Curie temperature is the critical temperature at which these magnetic moments change direction. In other words, at certain temperatures, the magnetic properties of some materials completely change. This can be explained by a symmetry-breaking mechanism.
In crystals, if you break the symmetry, which is a translational and rotational invariance, you get phonons. In superconductors, when you break a more esoteric symmetry (a gauge symmetry), you get Cooper pairs.
In the spontaneous symmetry breaking of a physical system, the laws of physics are invariant under a transformation, but the system itself changes.
The Nobel Prize in Physics was awarded in 2008 to Yoichiro Nambu for his work in 1960 in formulating a mathematical theory for understanding these symmetry breakings.

Supersymmetry helps to close gaps in the Standard Model.

Supersymmetry has been the dominant beyond-Standard-Model framework for many years. The theory relates the two basic classes of elementary particles, fermions and bosons, with each particle from one group having a “supersymmetric partner” in the other group.
In a perfect “unbroken” supersymmetry, each pair shares the same values for mass and internal quantum numbers (besides spin). For instance, a selectron would be a bosonic version of an electron, and would have the same mass energy, and in theory would be just as easy to find in a laboratory.
Yet, not a single supersymmetric partner has been discovered so far; if supersymmetry exists then the new particles it predicts would interact through the same forces as Standard Model particles, but would have different masses.
SUSY is a comprehensive framework that is both calculable and predictive, making it possible to build strong theory upon.
SUSY has many attractive theoretical properties, especially that it suppresses quantum corrections and is a spacetime symmetry rather than an ad-hoc postulation of extra degrees of freedom and “internal” symmetries.

SUSY models have many other useful features.

In many interesting models, the electroweak scale is derived from the SUSY-breaking scale, and the Higgs mechanism naturally takes place.
Once you have superpartners at the electroweak scale, SUSY models make sense up to around the Planck scale (~10¹⁹ GeV) where quantum gravity presumably becomes important.
SUSY models are the expected lower energy outcome of string theory, which might be the correct description for quantum gravity.
And in many well-studied models, the prediction of discovering all the superpartner particles comes with SUSY as they are connected to the electroweak scale.