Saturday 16 December 2017

gauge theory - How many fundamental forces could there be?


We’re told that ‘all forces are gauge forces’. The process seems to start with the Lagrangian corresponding to a particle-type, then the application of a local gauge symmetry leading to the emergence of the force bosons via the associated symmetry group.


But where did exactly four forces come from? Could new, perhaps supersymmetric particles hint at new fundamental forces? Is there a deeper theory which predicts what final set of forces we’ll eventually end up with?


Finally, is the concept of force in unified physics really that fundamental at all?



Answer




The very claim that there are "four fources" is an approximation. We know that the electromagnetic and the weak force have to be unified to an electroweak theory. So counting the electroweak theory as one force, there are just three known elementary forces.


The electroweak theory is based on the $SU(2)\times U(1)$ group which has two factors, but these two factors are not in one-to-one correspondence with the electromagnetism and the weak force, respectively.


The strong force with its $SU(3)$ group is another seemingly independent factors, except that there is evidence that all three non-gravitational forces get unified into a grand unified force of a GUT theory at high energies.


String theory unifies the non-gravitational forces with gravity, too.


Every vacuum of string theory predicts gravity described by GR plus extra non-gravitational forces. The number of factors and their Higgs-like breaking patterns are essentially random properties of the string vacua. According to the anthropic picture of the world, the number of low-energy forces is an accidental property of our world that could be different in different parts of the multiverse.


According to non-anthropic reasoning, the precise selection of our vacuum - including the fact that it has 4 low-energy forces - could be derivable from some more unique theoretical principles. However, this research program remains a wishful thinking as of 2011.


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