1+1 Dimensions

If you browse through the theoretical physics literature in the past decades, you will see a huge amount of work has been done in studying 1+1 dimensional theories.
To a non-physicist audience, this might seem somewhat ridiculous.
1+1 dimensions means just one point that can move back and forth on a line, this is so boring!!!.

The truth is that at the quantum level, not only they are not boring, but also most of the time they are unbelievably hard!

Then you might ask what is the point of studying these theories when we know that the world is not 1+1 dimensional?

The answer is quite simple. To face the real hard problem, we first prefer to warm up in simpler theories. The level of simplification achieved as we come down to 1+1 dimensions is astonishing!. There are some exactly solvable quantum field theories known in 2 dimensions. Also surprisingly, gravity in the absence of matter is both renormalizable and conformal in 2 dimensions which turns the almost impossibles to hard ones.

That was the initial motivation that brought physicists to 1+1 dimensions. But now, there are more to 1+1 dimensions than just a practice. They can be effective theories for higher dimensional theories under certain symmetries. More importantly, the deep relation of some fundamental concepts are much easier to see in 2 dimensions.

There are tons of other reasons to understand why studying 1+1 dimensions is not a waste of time.

As a consequence, I conclude I have a reasonable excuse for the readings that I am doing these days!!!