Elegance is the fuzziest aspect of beauty. It is often described as an element of surprise, the “aha-effect,” or the discovery of unexpected connections. One specific aspect of elegance is a theory’s resistance to change, often referred to as “rigidity” or (misleadingly, I think) as the ability of a theory to “explain itself.”I do not agree that grand unification and supersymmetry are beautiful. They require 100s of new parameters and particles in the theory, over the standard model's 20 or so.
By no way do I mean to propose this as a definition of beauty; it is merely a summary of what physicists mean when they say a theory is beautiful. General relativity, string theory, grand unification, and supersymmetry score high on all three aspects of beauty. The standard model, modified gravity, or asymptotically safe gravity, not so much.
But while physicists largely agree on what they mean by beauty, in some cases they disagree on whether a theory fulfills the requirements. This is the case most prominently for quantum mechanics and the multiverse.
A comment says:
A beautiful equation is also one that exhibits the fewest free parameters while explaining the most physics. That's why general relativity is beautiful while the Lagrangian of the Standard Model is ugly as hell. They both work, one by itself and the other by brute force, although I would never compare one with the other.No, I disagree. This is like saying that the periodic table of the chemical elements is ugly as hell, because it have 92+ elements and some irregularities. It was vastly simpler than any other categorization of the 1000s of known substances, and put them into simple patterns.
The standard model is just quarks, electrons, and neutrinos, with some flavors, generations, colors, and anti-particles, and some bosons for transmitting forces.