2.2 Duality Frames
The most important thing we have learned in string theory is the idea of duality.
- Almost everything interesting that we know about the theory is captured in the concept of duality. Duality is the general phenomenon that two very different-looking physical systems can nevertheless be identical.
- If we think about a space where we can vary all sorts of physical properties at will, we end up with “corner theories,” where a simple description of the physics emerges, analogous to reference frames in Einstein’s theory of relativity.
- The physics looks superficially different as we go from one frame to another, but the fundamental laws do not change.
- These corner theories are sometimes referred to as duality frames, essentially reference frames that are more simple to describe.
What are duality frame invariants?
- Just as in Einstein’s theory, the important concepts weren’t what a particular observer sees, but rather what remains invariant in all frames of reference, for instance, rest mass. So, what doesn’t change as we go from one duality frame to another?
- We can think of this idea using a familiar analogy: a phase diagram for some object. The object can be in a liquid, gaseous, or solid state, but of course it is still the same object. The invariant concept in this case is its constituent molecules.
- But, it turns out there are ways of varying the temperature and pressure for an object so that it goes from liquid to gas (and vice versa) without any noticeable phase transition—meaning the only way to describe this object invariantly is by its molecules.
- Similarly, the transitions between duality frames are gradual and there is no distinguishable separation when transitioning.
Are particles the basic building blocks of matter?
- This was a principle originally suggested by the ancient Greeks, the idea of an atom, some indivisible point-like particle that all matter is made of.
- In the modern era, this idea was extended to the idea of elementary particles. What we thought was the most indivisible particle (the atom) was discovered to be comprised of protons, neutrons, and electrons. And then the discovery of quarks changed our understanding of what the most fundamental particle was again.
- In the context of string theory, elementary particles are once again being replaced by extended objects like strings or membranes. So we know that the basic building blocks of matter are not point particles.