Why is it interesting?

Layman

The similarities between the vacuum of space and low-temperature phases of matter are legendary in physics. Not only are phases static,uniform quantum states, but their most subtle internal motions are physically indistinguishable om elementary particles very generally.3This is one of the most astonishing facts in science, and something students always find upsetting and difficult to believe. But they even­tually become convinced a er looking at enough experiments, for the evidence is plenti l and consistent. In fact, the more one studies the mathematical descriptions of cold phases, the more accustomed one gets to using the parallel terminologies of matter and space inter­changeably. Thus instead of a phase of matter we speak of a vacuum.Instead of particles we speak of excitations. Instead of collective mo­tions we speak of quasiparticles. The pre x "quasi" turns out to be a vestige of the historical battles over the physical meaning of these ob­jects and conveys no meaning. In private conversations one drops the pretense and refers to the objects as particle

[…]

The vacuum, when cooled from very high temperatures, is thought to undergo stepwise events called unification transitions, in which the known forces of nature split off sequentially from their fundamental parent. Similarly, holmium metal, a rare earth element, when cooled from very high temperature, first condenses into a liquid at 2993 degrees Kelvin, then solidifies at 1743 degrees, then develops a special kind of spiraling magnetism at 130 degrees, then tils the spiral to make weak ferromagnet at 20 degrees. Between 130 degrees and 20 degrees the pitch of the spiral varies continuously, as though it were a rubber screw being stretched along its axis. With each of these transitions the "forces" between electrons in the metal transmitted by various elastic distortions of the ordered state split off from the fundamental parent in beautiful and apt analogy with what occurs in the vacuum. The temperatures required to see the unification transitions of the vacuum cannot be achieved in the laboratory, or even in the centers of the largest stars, so the evidence for unification is indirect, but it nicely parallels what one would find in the tilted spiral magnet if one's experiments could reach only long length and time scales. One of the strongest of these bits of evidence is renormalizability, an effect that causes the accessible measurements to be simple and redundant (one measurement predicts another) but that at the same time is incapable of revealing anything about the forces at the top of the hierarchical tree.

[…]

There are numer­ous experimental indications that the vacuum emerges in a hierarchy of phase transitions in which the various forceS differentiate from each other….

If renormalizability of he vacuum is caused by proximity to phase transitions th the search for an ultimate theory would been doomend on two counts: it would not predict anything even if you found it, and it could not be falsified.

page 112 in "A different Universe" by Robert Laughlin

Student

• Grand Unified Theories by Graham Ross
• Grand Unification with and without Supersymmetry by Ed Witten
• Grand Unification with and Without Supersymmetry And Cosmology Implications by C Kounnas et. al.
• http://users.physics.uoc.gr/~rosen/projects/gutFive.pdf

Researcher

• The Algebra of Grand Unified Theories by John C. Baez, John Huerta
• Group Theory for Unified Model Building by R. Slansky
• Model Building and Phenomenology in Grand Unified Theories by Tomas E. Gonzalo Velasco
• http://jakobschwichtenberg.com/resources-that-helped-me-understand-grand-unified-theories/

Examples

Example1

Example2:

FAQ

Why does a simple group mean that we have just one coupling?

In QFT we get for each simple group a coupling. In contrast consider the couplings in a non-simple group:

This Lagrangian is actually invariant under a larger U(2) = U(1) × SU(2) symmetry. But, as we will come to understand, there is no point in considering non-simple groups such as U(N) in quantum field theory. For example, in a gauge theory the coupling constants for the U(1) and SU(2) subgroups will in general be different; even if we set them equal at one scale, they will run differently. Moreover, the U(1) symmetry in Lagrangians such as Eq. (25.1) will often be violated by a quantum effect called an anomaly, to be discussed in Chapter 30. Thus, we will restrict attention to the simple SU(N) subgroups.

from Quantum Field Theory by Schwartz

Do the Standard Model gauge couplings really do not unify?

No! The hypercharge normalization is not fixed in the standard model and if we choose a normalization $k_Y= 11/3$, the gauge couplings meet perfectly around $10^{17}$ GeV. Two gauge couplings $g_2$ and $g_3$ always meet at a point as long as they aren't parallel and because the normalization of $g_1$ isn't fixed we can adjust it appropriately. (This is mentioned, for example, here: https://arxiv.org/pdf/0903.3929.pdf)

A nice overview of how the hypercharge normalization is fixed for different GUT groups, see Table 1 in https://arxiv.org/pdf/hep-ph/0606012.pdf

History

Criticism

"Physics is littered with the corpses of dead unified field theories." Freeman Dyson

"The bad news is that those people who went off to detect proton decay never found it! It became clear in the mid-1980s that the proton lifetime was at least $10^{32}$ years or so, much larger than what the SU(5) theory most naturally predicts. Of course, if one is desperate to save a beautiful theory from an ugly fact, one can resort to desperate measures. For example, one can get the SU(5) model to predict very slow proton decay by making the grand unification mass scale large. Unfortunately, then the coupling constants of the strong and electroweak forces don't match at the grand unification mass scale. This became painfully clear as better measurements of the strong coupling constant came in." from This Week's Finds in Mathematical Physics (Week 119) by John Baez

“People can construct models with higher symmetries and stand on their nose and try to avoid proton decay,” Nanopoulos said. “OK, you can do it, but … you cannot show it to your mother with a straight face.” https://www.quantamagazine.org/20161215-proton-decay-grand-unification/</blockquote> —- * https://physics.stackexchange.com/questions/79064/how-does-the-super-kamiokande-experiment-falsify-su5 </tabbox>