I was reading the book "A Fortunate Universe" by Geraint Lewis and Luke Barnes and something caught my attention:
At page 195 the authors say that universes with different symmetries could be modeled and they would have dramatic results like having different conservation laws.
I asked Mr. Lewis if he could give me more information about this and he told me this:
We can play with equations and add or subtract dimensions in our universe – like adding another time dimension to relativity. These other hypothetical universes could have different symmetries, so things like electric charge might not be conserved, while kinetic energy is. This would give very different physical outcomes. And yes, we could get very different physical laws with interactions that we just don’t see in our universe.
He mentioned that these universes with different symmetries and non-conserved quantities would be the result of "playing" with the dimensions of mathematical models of universes. This reminds me a lot to what happens in String Theory compactification or in M Theory.
And also, at another book by Kurt Sundermeyer called "Symmetries in Fundamental Physics", he says at page 466:
It is an astounding state of affairs that string theories in 10 dimensions vibrate with symmetries, but that after compactification we may get into worlds with no symmetries at all
I have always read that in string theory landscape the different vacua would have the same symmetries but they would be broken differently, or at least that is what I have understood until now. But I have never read anything about vacua with different fundamental symmetries in string theory.
Therefore, does String Theory or M Theory propose that these universes with very different fundamental symmetries may exist? Do any of these theories speculate that universes with different kinds of symmetries (different global symmetries, local symmetries, gauge symmetries...etc) may exist?