Vice presidential buzz is rising for businessman Vivek Ramaswamy after Wednesday’s Republican primary debate, which, in the absence of the front-runner, President Trump, became as much of an opportunity to audition for the presidential nomination as it was to jockey for the no. 2 spot on a Trump ticket.

Critical response suggests Mr. Ramswamy appeared to emerge from the debate with the best performance, even if viewers were far from unanimous in agreeing who put on the best show.

Because of that, and the fact that Mr. Ramaswamy is one of the few candidates Mr. Trump has spoken of positively in the past, speculation immediately turned to the prospect that the entrepreneur might make the short list of vice presidential picks.

The debate “doesn’t seem to have shifted the field of who could be president,” an analyst at Washington University at Saint Louis’s Decision Desk HQ, Liberty Vittert, tells the Sun. Yet “it definitely brings to light the continued Trump-leaning majority,” she said, “and potentially gives Ramaswamy a boost for VP positioning.” 

On the debate stage, Mr. Ramaswamy was also far more eager than other candidates to show his fealty to Mr. Trump, calling on his competitors to commit to pardoning Mr. Trump if he is convicted.

“If people at home want to see a bunch of people blindly bashing Donald Trump without an iota of vision for this country, they can just change the channel to MSNBC right now,” Mr. Ramaswamy said.

Other candidates, such as a former governor of South Carolina and ambassador to the United Nations, Nikki Haley, posted breakout performances during the debate. Yet she was also critical of Mr. Trump, which could very well destroy any chances of her being considered as a vice presidential pick.

“Trump is the most disliked politician in America,” Ms. Haley said. “We can’t win a general election that way.”

A political scientist at John Jay College, Brian Arbour, tells the Sun that simply being on the debate stage may disqualify a candidate for the vice presidential spot. “I’m not sure he’s picking someone who’s vied for the same job that he, frankly, feels entitled to,” Mr. Arbour said.

“There were two things constructive for picking Mike Pence in 2016,” Mr. Arbour tells the Sun. “One is that he didn’t run for president. … The second is that he picked a conventional Republican, which he regretted.”

Three vice presidential prospects who were not on the debate stage stand out: Governor Noem of South Dakota, Congresswoman Marjorie Taylor Greene, and a TV host, Kari Lake. All three weighed in on the debate in some way.

In some parts of the country, ads from Ms. Noem filled the commercial breaks during the debate with her “Bright Side” campaign, which features ads in which Ms. Noem dresses up as a variety of different professionals to attempt to convince people to move to South Dakota.

Ms. Noem has previously said that she would consider being Mr. Trump’s running mate if he asked her, and her interest in the vice presidency has been often discussed.

In conversation with Right Side Broadcasting Network, Ms. Greene claimed to be an “official surrogate for President Trump,” before saying that she was “blocked from entering the Fox News media spin room,” adding that it was “censorship from Fox News.”

Ms. Greene has also said in an interview with the Atlanta Journal Constitution that she would be interested in being on Mr. Trump’s ticket if the spot was offered to her.

Another acolyte of Mr. Trump who may be auditioning for the vice presidential spot and possibly running for Senate in 2024, Ms. Lake, a losing Arizona gubernatorial candidate, commented on the debate from the sidelines.

“President Donald J. Trump: the first man in history to win a debate without even being on the stage,” she tweeted.

Ms. Lake also made a point of defending Mr. Trump regarding his attempt to overturn the 2020 election results on January 6, 2021, and earlier, saying that Fox News gave Mr. Pence “a platform to misrepresent what Grassroots Americans were actually asking him to do on January 6th, 2021.”

“It’s a personal and idiosyncratic choice and therefore hard to handicap,” Mr. Arbour said of the non-debaters. “All of those seem possible and I do think there’s a good chance he’ll select a woman or a minority.”