# Physical Motivation for Supersymmetry

## Main Question or Discussion Point

How was supersymmetry discovered? 13:00 And what were the original motivations for it? Is there some kind of intuitive way to look at and work with the formulas? For instance, in the theory of differential forms, the scalar product of two 1-forms U and V is *(U ∧ *V) = UiVi. It is useful to think of this as being similar to the product of a complex number z and its conjugate z*, giving zz* = r2. However far the analogy might go, this kind of thing certainly helps to give some vague idea of what the hodge star is doing in U ∧ *V. As far as I know, supersymmetry was discovered in a formal way, but I want to know, are there any physical motivations or helpful ways to look at the formulas? Take the superfield

$$X^\mu = x^\mu + \theta \psi_+^\mu + \bar{\theta} \psi_-^\mu + \theta \bar{\theta} F$$

Can this be thought of as some kind of four component object? Or take the canonical momentum

$$\Pi_m^\mu = \partial_m x^\mu - i\bar{\theta}^I \Gamma^\mu \partial_m \theta^I$$

with action S1 + S2

$$S_1[x, \theta] = \frac{1}{8\pi} \int_\Sigma g^{mn} \eta_{\mu\nu} \Pi_m^\mu \Pi_n^\nu$$

$$S_2[x, \theta] = \frac{1}{4\pi} \int_\Sigma \{ -i \ dx^\mu \wedge (\bar{\theta}^1 \Gamma_\mu d\theta^1 - \bar{\theta}^2 \Gamma_\mu d\theta^2) + \bar{\theta}^1 \Gamma_\mu d\theta^1 \wedge \bar{\theta}^2 \Gamma_\mu d\theta^2 \}$$

In the expression for ##\Pi_m^\mu##, we have two similar things ##\partial_m x^\mu## and ##\partial_m \theta^I## combined together. Can this be thought of as some kind of two-component object like x + iy, where the role of i is played by ##i\bar{\theta}^I \Gamma^\mu##?

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MathematicalPhysicist
Gold Member
It's like we have "man" and we would like him to have a superpartner let's call him "superman"... Fra
A short comment: From my perspective, a possible general "physical motivation" for ANY of the "weird" or hard-to-understand-in-mechanical-realist-ways symmetries between theories is this:

If you adhere to the view that the laws of physics are selected as way to provide optimal representations in observing systems, during a number of constraints, then these symmetries can be physically motivated first of all as simply equivalent ways of coding the same information, but selection is made based that for a given observer, only one perspective is the right one. So if we envision abstract "strange" observers, two observers could end up seeing different things, one sees fermions and one sees bosons. The interestin thing is when these observes are forced to communicate the results, and there may be pressure on observers to revise their codes.

IMO, this is loosely speaking what actually happened at least in my head, when you try with the klein gordon equation for an electron, and and up beeing force to make a transformation (change of dependend variables) and get the dirac equation, and the invention of fermions. This is also a hint of actual transformation that mixes internal structures with spacetime dynamics, motivation for that is the same. The spacetime is just relations between interacting systems its not real as a substance; and the systems internal coding can easily change the relations. All this is of course totally impossible to understand in a mechanical old realist way.

/Fredrik

Staff Emeritus
2019 Award
Supersymmetry was originally proposed as a pre-QCD explanation of why there were mesons and baryons.

• ohwilleke, dextercioby and arivero
MathematicalPhysicist
Gold Member
Supersymmetry was originally proposed as a pre-QCD explanation of why there were mesons and baryons.
So what is the QCD explanation for there are mesons and baryons?
https://arxiv.org/pdf/1802.08131.pdf

It seems QCD requires an infinite number of gluons to mediate the strong force, something that physicists don't like because they prefer a finite description of nature.

Tough luck physicists! Staff Emeritus
2019 Award
what is the QCD explanation for there are mesons and baryons?
There are qqbar and qqq color-neutral combinations.

• ohwilleke
MathematicalPhysicist
Gold Member
So what is the QCD explanation for there are mesons and baryons?
https://arxiv.org/pdf/1802.08131.pdf

It seems QCD requires an infinite number of gluons to mediate the strong force, something that physicists don't like because they prefer a finite description of nature.

Tough luck physicists! Actually according to the paper there should be an infinite number of quarks.
Here's the preface:
Just as Quantum Electrodynamics describes how electrons are bound in atoms by the electromagnetic force,mediated by exchange of photons, Quantum Chromodynamics (QCD) describes how quarks are bound insidehadrons by the strong force, mediated by exchange of gluons. At face value, QCD allows hadrons constructedfrom increasingly many quarks to exist, just as atoms with increasing numbers of electrons exist, yet suchcomplex constructions seemed, until recently, to not be present in nature. In what follows we describeadvances in the spectroscopy of mesons that are refining our understanding of the rules for building hadronsfrom QCD.

It's a good idea that I decided to do my thesis on QCD and not on SUSY or SUPERSTRING.

Just need to start reading Mueller's book on Perturbative QCD.

MathematicalPhysicist
Gold Member
Well it really depends I see there are many books by string theorists also in QCD.

For example the red book by Sonnenschein and Frishman called Non-Perturbative Field Theory.
But it seems you first need to know some CFT from the classic book in CFT (quite heavy lifting indeed).

But I prefer first to finish with GR by Schutz book, and then proceed to Muller's and perhaps also Collins' textbook.

How was supersymmetry discovered? 13:00 And what were the original motivations for it?
The GL paper

http://www.jetpletters.ac.ru/ps/1584/article_24309.shtml

one of the first papers on what became known as supersymmetry, introduced the idea by noting that only a fraction of the possible interactions invariant under the Poincare group are realized in nature, hence it may be that the fraction of realized interactions obey a higher level of symmetry (related to the Poincare group) the others don't.

With this as a basis, it is conspicuous that one constructs spin representations of the Lorentz sub-group of the Poincare group, but the translation generators are kind of just sitting there, so it's natural to consider a spin analogue/'representation' of the translation generators just as one constructs representations of the Lorentz generators, but this would violate spin-statistics using commutators however anti-commutators are natural with spin representations so voila, giving you (1a) and (1b) of the paper.

• ohwilleke and dextercioby
ohwilleke
Gold Member
The GL paper

http://www.jetpletters.ac.ru/ps/1584/article_24309.shtml

one of the first papers on what became known as supersymmetry, introduced the idea by noting that only a fraction of the possible interactions invariant under the Poincare group are realized in nature, hence it may be that the fraction of realized interactions obey a higher level of symmetry (related to the Poincare group) the others don't.

With this as a basis, it is conspicuous that one constructs spin representations of the Lorentz sub-group of the Poincare group, but the translation generators are kind of just sitting there, so it's natural to consider a spin analogue/'representation' of the translation generators just as one constructs representations of the Lorentz generators, but this would violate spin-statistics using commutators however anti-commutators are natural with spin representations so voila, giving you (1a) and (1b) of the paper.
Supersymmetry made all sorts of sense as a plausible thing for Nature to have done. But, the collider data makes it every more clear that Nature didn't do that.

Also, the other big motivation for supersymmetry over other plausible conjectures was to explain the hierarchy "problem", Supersymmetry automatically eliminates the hierarchy problem in what is mathematically a very straightforward and direct way.

But, it is now clear that even if supersymmetry exists at very high energy scales beyond the reach of existing colliders, that supersymmetric particles so heavy that they are beyond the ability to existing experiments to detect would not meaningfully address the hierarchy problem notions that initially motivated the theory.

The non-existence of supersymmetry (which isn't truly ruled out and probably never will be completely because it has so many parameters that can be tweaked) is huge because not only does it rule out the low level effective supersymmetry and supergravity theories, it also rules out most, or all, favored string theories, and a great many GUTs and TOEs.

This suggests that the heartland of fundamental theoretical physics, which is string theory, is not just a case of having taken a slightly wrong path. It suggests that the heart of current fundamental theoretical physics work is metaphorically on the wrong continent and nowhere close to what we really want to discover.