A right to work state is one in which a person can not be forced to join a union. You are referring to an "At will" state. And you are correct, no cause required to terminate.
There are a few limitations...
Terminations initiated by the employer must not be discriminatory or in violation of specific Federal or state laws. For example, the employer is legally prohibited from taking any “adverse employment action” against an employee because of his or her race, gender, age, disability, national origin, or any other legally protected characteristic or activity. Protected activities include, but are not limited to:
(Source)• Filing a complaint of discrimination on the basis of race, color, religion, age, sex, national origin or disability.
• Filing a workers’ compensation claim.
• Jury service.
• Refusing to perform an illegal act.
• Reporting violations of law.
More info at: Pay and Policies - General
Cheers! M2