Physicists like symmetries. Emmy Noether taught us that symmetries result in conserved quantities. For most “ordinary” symmetries, these conserved quantities are (basically) numbers of particles.
For example, if you have a bunch of atoms in a box, the mathematical description of the box has a certain “symmetry” that enforces the dynamical statement that the number of atoms in the box can’t change, and that you can’t lose an atom!
Now, this is fine if you only care about particles. But, many interesting systems have “extended objects” — e.g. strings — which are also conserved.
“My favorite example is ordinary Maxwell electromagnetism, where magnetic field lines are strings that cannot end.”— Nabil Iqbal, Theoretical Physicist and Associate Professor at Durham University
What is the symmetry principle enforcing the conservation of higher dimensional objects? Nowadays, we call these “higher form symmetries”, and they were explained by Davide Gaiotto and colleagues in their 2014 paper, that influenced Nabil Iqbal’s research greatly.
“The upshot is that, if you ever have extended objects that can’t break or vanish — gauge theory flux tubes, cosmic strings, magnetic field lines — you probably have one of these higher-form symmetries playing an important role.”— told Nabil Iqbal
The idea behind higher-form symmetries is simple: just as ordinary global symmetries result in conservation laws for particles, theories that are invariant under higher-form global symmetries possess conservation laws for extended objects, such as strings or flux tubes.
“We can now try and use these new symmetries to organize our understanding. In the recent work with John, we build a Landau-Ginzburg theory for such symmetries, where we try and describe the physics close to a point where one of these symmetries is” “about” to break.”— told Nabil Iqbal
Just as normal Landau-Ginzburg theories describe the condensation of particles, this new framework has to describe the condensation of “strings”. This is complicated but fun, and they tried to get a grasp of it using these new symmetries and principles of effective field theory.
“By the way, these are “not” gauge symmetries; gauge “symmetry” is perhaps a lousy name for something that is not really a symmetry at all. But a lot of gauge theories happen to host extended objects, and so can be nicely understood in this framework.”
If you wanna know more, just check out the video given below, Nabil Iqbal have given some online talks on it.
Nabil Iqbal, John McGreevy, “Mean string field theory: Landau-Ginzburg theory for 1-form symmetries”, Arxiv, pp. 1-47, 2021.
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