I'm a math student in senior year. I want to know about CFT(as the title explained). For related knowledge, I've learned basics about Differential Geometry, Differential manifolds. I want to just "touch", or get a sketch of this field, not to dive in for jargon and details. Are there any books, or papers easy enough for me to understand?
Why asking this:
I need to know CFT mainly because my Bachelor degree graduating paper, in which I'm supposed to get a basic understanding and a picture of modern math developments in Quantum Field Theory. CFT is an important branch in QFT so I must learn it briefly. But I have no background in QFT basics, nor in Quantum mechanics (I can learn them, though, given some time). So I came to ask if any of you know some material suitable for me.
Details that might help:
Below is a picture of Blumenhagen and Plauschinn 's Introduction to Conformal Field Theory With Applications to String Theory. The red-underlined equation, for example, is something I can't understand. What is $\varphi^*$ ? What is $g$ and $g'$ ? I'm thinking it may appears in some preliminary materials that I forgot or need to learn.