What gui library is used by sublime text editor?

Sublime Text 2 is mostly coded in C++ and uses a custom UI toolkit. Here is the author, Jon Skinner, explaining it: http://news.ycombinator.com/item?id=2822114.

I keep meaning to write a blog post with some details on this, but as with many things, I usually end up coding instead. Sublime Text 2 is almost entirely C++ (with a smattering of Objective C for Cocoa and Python for plugins). Coding is generally fairly straight forward: code on one platform (mostly Linux at the moment, but I switch around frequently), and then make sure it still compiles elsewhere. Sublime Text 2 itself uses a custom UI toolkit. There are a lot of apps where this may not make sense, but it's not such an unreasonable choice for Sublime Text, where I always knew that a lot of the UI controls were going to have to be custom no matter the toolkit (e.g., the text control and tab controls). The UI toolkit sits on top of a cross platform abstraction layer, which is more a union of platform functionality rather than lowest common denominator.

a little Googling suggested it is using the Sublime GUI, which judging by the Debian source package is written in C++.

then again, running strings on the Linux sublime_text binary shows the following shared libraries (equivalent of Windows DLLs) which might suggest gtk:

/lib/ld-linux.so.2libgtk-x11-2.0.so.0libgdk-x11-2.0.so.0libatk-1.0.so.0libgio-2.0.so.0libpangoft2-1.0.so.0libpangocairo-1.0.so.0libgdk_pixbuf-2.0.so.0libcairo.so.2libpng12.so.0libpango-1.0.so.0libfreetype.so.6libfontconfig.so.1libgobject-2.0.so.0libgmodule-2.0.so.0libgthread-2.0.so.0librt.so.1libglib-2.0.so.0libpthread.so.0libdl.so.2libutil.so.1libm.so.6libX11.so.6libstdc++.so.6libgcc_s.so.1libc.so.6libgio-2.0.solibgio-2.0.so.0module.so

this also suggests gtk.

It might not be written in Python. The reason you see Python code is users can write scripts/plugin in Pythons to extend Sublime Text. I suspect it is written in C++ with GTK as GUI toolkit.