# Why is (anti)-holomorphicity considered in physics?

As a mathematician, holomorphicity is an extremely good property that provides rigidity, finite dimensionality, algebraicity. etc to whatever theory that's considered. I'm curious about why (anti-)holomorphicity is considered in physics.

As an example, apparently holomorphic representations of $$SL(2,\mathbb{C})$$ apply to physics, while weaker kinds of representations are of interest in math as well.

As another example, 2D conformal field theory models fields as meromorphic functions. Though conformality almost equals holomorphicity in 2D, I'm still curious why picking "conformal" in the beginning?

Q. Do people consider them because they have well-developed mathematical background and thus allow us to say something interesting, or there are deeper reasons behind it?

• This post (v2) seems somewhat broad and opinion-based. Complex function theory is used in almost all areas of physics basically because it is very powerful. May 17 '20 at 19:56
• That's it? And why you think this thread can have several valid answers? May 17 '20 at 19:58