How do LED light bulbs work?
There are several circuits on the internet from noatable sources that show how LEDs can be powered directly from an AC supply without a transformer. Here's one from ON semi: -



And here is the document it came from. The document is entitled "High Current LED - capacitive drop drive application note".

Here is another interesting article, this time from EDN. It shows the following diagram, again transformerless: -



And another article and circuit here: -