Can I publish a research paper without notifying my supervisor (the corresponding author)? My professor doesn’t want to publish and he keeps delaying it. I had an intense argument with him and I feel that if he will publish, he will not include me. He is quite rude to me recently, although I worked so hard on two projects under his supervision. It has been about two years and he didn't publish my work.

Do Journals contact the corresponding authors when a research paper is submitted? What happened if (for example) I published an article without notifying a corresponding author and he found out? What could happen?
No, you absolutely may not do this.  Every author must consent to the publication of an article.

If he finds out, he could have the journal withdraw the article.  They would typically publish a notice about this, which would effectively inform the whole world that you had done something unethical.  That is a potential career killer.  Additionally, a serious breach of academic ethics like this could cause you to be expelled from the university where you study.

Many journals do directly contact every listed author, to prevent this sort of situation.  (For instance, in many cases every author has to sign a copyright form.)  Others will ask the submitting author to certify that they have the consent of all other authors.