Brad Raffensperger, the two-term Republican secretary of state, joins a primary that also includes the state’s lieutenant governor and attorney general.

© Dustin Chambers for The New York Times

Mr. Walz raised his national profile with a run for vice president. He has suggested that an additional term as governor would rule out the prospect of him running for president in 2028.

© Emily Elconin for The New York Times

Mr. Walz raised his national profile with a run for vice president. He has suggested that an additional term as governor would rule out the prospect of him running for president in 2028.

© Emily Elconin for The New York Times

Geoff Duncan could prove to be a wild card in an election next year that will be a crucial test for Georgia’s relatively new status as a swing state.

© Ruth Fremson/The New York Times