Section 3. No person shall be a Senator or Representative in Congress, or elector of President and Vice President, or hold any office, civil or military, under the United States, or under any State, who, having previously taken an oath, as a member of Congress, or as an officer of the United States, or as a member of any State legislature, or as an executive or judicial officer of any State, to support the Constitution of the United States, shall have engaged in insurrection or rebellion against the same, or given aid or comfort to the enemies thereof. But Congress may, by a vote of two-thirds of each House, remove such disability.

(Emphasis naturally not in the original.)

It depends on if you can claim they gave aid or comfort to the people storming the capitol. Many of the justices might be questionable for other reasons, but unless they were actively there or publicly supportive of it, I don't think they'd qualify. Plus, who's going to rule on it, the other justices?

That being said, in 2022, there was a case of a politician in New Mexico being barred from public office for life for being supportive of Jan 6th. Apparently it's the first time this has happened since 1869 (and remained upheld).

Expect multiple lawsuits if this paper's conclusions are acted upon.

“Section 3’s disqualification rule may and must be followed — applied, honored, obeyed, enforced, carried out — by anyone whose job it is to figure out whether someone is legally qualified to office,” the authors wrote. That includes election administrators, the article said.

Professor Calabresi said those administrators must act. **“Trump is ineligible to be on the ballot, and each of the 50 state secretaries of state has an obligation to print ballots without his name on them,” **he said, adding that they may be sued for refusing to do so.

[…]

“The question of should Donald Trump go to jail is entrusted to the criminal process,” he said. “The question of should he be allowed to take the constitutional oath again and be given constitutional power again is not a question given to any jury.”