Nikki Haley staked out a clear, hawkish vision. Ron DeSantis avoided risks. And the night’s glaring absentee, Donald Trump, again emerged untouched.It was the undercard that underwhelmed.The third straight Republican presidential debate that former President Donald J. Trump has skipped — choosing instead to rally with supporters a few miles away — represented a critical and shrinking chance for his rivals to close his chasm of a polling advantage.And with only five candidates on the stage for the first time — Chris Christie, Ron DeSantis, Nikki Haley, Vivek Ramaswamy and Tim Scott — they all had far more time to speak.Yet they had precious little to say about Mr. Trump, even when given the chance just over two months before the Iowa caucuses.They sparred in a substantive debate that dissected disagreements over aid to Ukraine, Social Security, confronting China, banning TikTok and how to approach abortion less than 24 hours after Republicans suffered their latest electoral setbacks driven by the fall of Roe v. Wade.But there was something surreal about such detailed discussions unfolding among candidates who seem so far from the Oval Office — even Mr. DeSantis and Ms. Haley, who asserted themselves as the leaders of the non-Trump pack.Here are six takeaways from a debate in Miami that may best be remembered for Ms. Haley snapping at Mr. Ramaswamy, “You’re just scum.”Haley came out swinging.Ms. Haley, the former U.S. ambassador to the United Nations, said that there would be no Hamas without Iran.Scott McIntyre for The New York TimesNikki Haley emerged as a power center on the debate stage, giving a forceful performance that took advantage of the night’s focus on foreign policy to present a clear and hawkish vision of America’s role in the world.Leaning into her experience as the U.S. ambassador to the United Nations, she staked out expansive, interventionist positions that cut against Mr. Trump’s “America First” foreign policy vision.She backed Ukraine to the hilt. She said she would support military strikes against Iran. And she said the United States needed to support Israel with “whatever they need and whenever they need it.”Most of the other candidates gave versions of the same responses — but Ms. Haley had the edge of having represented the United States on the world stage.When the candidates were asked what they would urge Prime Minister Benjamin Netanyahu of Israel to do at this moment, Mr. DeSantis said he “would be telling” him to eliminate Hamas. Ms. Haley said she did, in fact, tell Mr. Netanyahu to “finish them.”As Ms. Haley vies with Mr. DeSantis to establish herself as the field’s Trump alternative, some of the party’s biggest donors were closely watching her performance as they weighed whether to spend millions on her behalf in a desperate final effort to beat Mr. Trump.Ms. Haley’s competitors recognized her rising status by taking aim at her.DeSantis is still playing it safe in a game he’s losing.The Florida governor criticized Donald Trump’s absence from the debate stage.Scott McIntyre for The New York TimesIt seemed, for a moment, as if this would be a different kind of debate for Mr. DeSantis. His opening answer affirmatively outlined how he would be better than Mr. Trump.“He should explain why he didn’t have Mexico pay for the border wall,” Mr. DeSantis began. “He should explain why he racked up so much debt. He should explain why he didn’t drain the swamp.” He went on to say that Mr. Trump promised “winning” only to have his party endure years of “losing,” including on Tuesday.“In Florida, I showed how it’s done,” Mr. DeSantis declared, trying to take hometown advantage of a debate held in Miami.But then he mostly left Mr. Trump untouched, satisfied to prosecute his own case and push back on rivals like Ms. Haley. It was the same strategy he used in the first two debates, with little traction gained.Mr. DeSantis is plainly more comfortable than in the first debate. Yet he surprisingly left unsaid a development that his campaign has advertised as a game changer: the endorsement this week of Gov. Kim Reynolds of Iowa.You can’t debate someone who isn’t there.Chris Christie took the sharpest aim at Mr. Trump, but in his absence the five contenders were left to tear one another down, with varying levels of nastiness.Maansi Srivastava/The New York TimesThe candidates again did little to aggressively contrast themselves with Mr. Trump, who has made himself unavailable for direct sparring by refusing to stand onstage with his rivals or, for the most part, appear with them at multicandidate gatherings on the campaign trail.Without Mr. Trump present, the five contenders were left to tear one another down, with varying levels of nastiness.The first question to the candidates was the fundamental one most of them have struggled to answer to Republican voters: why they, and not Mr. Trump, should be the nominee.Mr. Christie, as expected, was the sharpest in his attack, arguing that someone who faces Mr. Trump’s criminal charges “cannot lead this party or this country.”But Mr. DeSantis took only a brief swipe. Ms. Haley praised Mr. Trump’s presidency, then criticized him, saying that he had gone “weak in the knees” on Ukraine and that his time had passed. Mr. Ramaswamy defended Mr. Trump in passing. And Mr. Scott talked about himself.Nikki Haley said that she doesn’t believe Trump is the “right president now.”NBC NewsThat was almost the extent of efforts to chip away at the runaway front-runner. Nearby, Mr. Trump held a rally in Hialeah, Fla., remarking at one point that his rivals were “not watchable.”For months, the candidates have struggled to find a way to force him into the ring with them, with Mr. Christie threatening to follow him on the campaign trail and Mr. DeSantis, in recent days, lobbing crass responses to Mr. Trump’s brutal taunts. In the third debate, none of them figured out how to make it work.This debate got personal.Vivek Ramaswamy fought with the NBC moderators and the head of the Republican National Committee, Ronna McDaniel, whom he urged to resign.Maansi Srivastava/The New York TimesAfter three debates, this much is clear: Some of the candidates onstage really don’t like one another.The most loathed appears to be Mr. Ramaswamy, who from the start fought not just with the rivals flanking him but also with the NBC moderators and the head of the Republican National Committee, Ronna McDaniel, whom he urged to resign in his opening statement.At times, Mr. Ramaswamy almost seemed to be doing Mr. Trump’s bidding, attacking NBC’s past coverage of the former president’s scandals.He made acidic attacks on Ms. Haley, mocking her foreign policy and calling her “Dick Cheney in three-inch heels.” He slipped in a crack about Mr. DeSantis’s footwear, suggesting that the Florida governor, too, was wearing lifts. Mr. DeSantis ignored him. Ms. Haley said hers were five inches and “for ammunition.”When Mr. Ramaswamy later invoked her daughter’s use of TikTok, she demanded, “Leave my daughter out of your voice,” and then added in almost disbelief about the exchange, “You’re just scum.”During a confrontation over TikTok, Nikki Haley snapped at Vivek Ramaswamy after he scolded Ms. Haley over her daughter’s use of the app.Scott McIntyre for The New York TimesAbortion remains a Republican quagmire.The crowd at Wednesday’s debate.Maansi Srivastava/The New York TimesAfter Tuesday’s defeats, the Republican candidates knew they would face questions about the way forward on abortion. But they mostly seemed uncertain what to say.“We’re better off when we can promote a culture of life,” said Mr. DeSantis, who signed a six-week ban in his state. He said little at all about what his party should do or what he would do as president. “At the same time, I understand that some of these states are doing it a little bit different.”Ms. Haley described herself as opposed to abortion, but said that passing national restrictions would be virtually impossible, arguing that it’s crucial to be “honest” with the public. At times, Ms. Haley seemed to be trying to appeal to general-election voters. “I don’t judge anyone for being pro-choice,” she said. It was the kind of line that makes Democratic strategists worry about her strength if she were to win the nomination — but also one that the G.O.P. base is unlikely to welcome.It all amounted to a reminder that Republicans, after decades of campaigning against abortion rights, have yet to figure out what to say after finally getting their wish through a Supreme Court that Mr. Trump — who also won’t say where he stands on a national ban — reshaped.Was this Tim Scott’s swan song?Tim Scott said “diplomacy only“ in the Israel-Hamas war was “a weak strategy.“Scott McIntyre for The New York TimesMr. Scott qualified for this debate by the narrowest of margins, with only a single poll — the legitimacy of which some of his rivals have privately disputed — ensuring his spot. But the thresholds will be higher for the next debate in December, and Mr. Scott’s allies acknowledge that he needs to something, anything, just to remain a factor.It’s hard to imagine that he did anything on Wednesday night to change his trajectory. He stuck to the same messages he has been hitting throughout the campaign. He described an America in need of spiritual healing and a return to Judeo-Christian values.He received more attention for what he did after the debate than for anything he said during it. Mr. Scott, 58, has never been married, and entire newspaper stories have been dedicated to a mysterious girlfriend who had never been seen with him in public.Until he brought her onstage.Michael Gold More