Can I publish a research paper without notifying my supervisor (the corresponding author)?
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.