Legal Question in Employment Law in California

The answer is "no." The exceptions to that "no" would be if you are a government employee or if you have a specific contract of employment that requires "good cause" for termination of employment. Your gut response is probably, "What?! They can treat people like that?"

Employment "at will" has may exceptions, and one of them in California at one time had teeth: the "implied contract" exception. That theory was eviscerated by the CA Supreme Court in Guz v. Bechtel, published over a decade ago. There are still strong anti-discrimination and anti-retaliation laws, but old fashioned fairness is now low on the list of rights.

You reference "seeing" the complaint, implying thereby that it is a written complaint. You do not deny the employer has verbally informed you of the basics of the complaint. If the company has a written policy of fairness, with warning that performance is unsatisfactory, your internal recourse is to assert the policy to get at least enough information to form your own written rebuttal, which you should then request to have placed in your personnel file.

I also always weigh the possibility that the charge is so completely bogus, and the employer knew or should have known it was false, yet proceeded to discipline you, that the original complainant and the employer have maliciously committed defamation of your work character.