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The Republican debate stage will be noticeably smaller when the candidates gather in Charleston, S.C., on Thursday night for their first debate of the year.

On Monday, Fox Business Network, the host of the debate, announced on “Lou Dobbs Tonight” the qualifiers for the main stage, and Senator Rand Paul of Kentucky and Carly Fiorina — who have both been slipping in recent polls — did not make the cut.

The candidate lineup for the 9p ET @FoxBusiness #GOPDebate on Thursday, January 14th: pic.twitter.com/mKHykPBzdm — Fox News (@FoxNews) January 12, 2016

To qualify for the prime-time debate based on the network’s criteria, the candidates had to either have placed in the top six in national polls, based on an average of the five most recent national polls recognized by Fox News, or have placed within the top five based on the average of the five most recent state polls in Iowa or New Hampshire. Fox Business Network said that it used 17 polls to determine its final lineup.

Being left off the main stage is a huge blow for Mr. Paul’s campaign. Once seen as the rising star in the Republican Party, Mr. Paul has struggled in the polls as his noninterventionist stance on foreign policy became a liability after the terrorist attacks in Paris in November. He has also seen his status as an outsider and anti-establishment candidate overtaken by Senator Ted Cruz of Texas and Donald J. Trump.

Minutes before the announcement, Mr. Paul said in an interview with CNN that after being told he would not make the main debate, he informed the network that he would not participate in the undercard debate, reiterating a promise he had made last month.

“I’ll be taking my campaign directly to New Hampshire and Iowa,” the senator told CNN. “I’m not going to be in South Carolina.”

Mike Huckabee and Rick Santorum were also left out of the prime time debate and were invited to the “under card” forum.

Mrs. Fiorina saw her campaign surge in the polls after her strong performance in the first undercard debate, which was followed by another well-received performance in the second prime-time debate. But she struggled to translate her success in the debates into better polling numbers.