SAUDI ARABIA was only going to tolerate the advances of the Iranian-backed Houthi rebels for so long. Early on the morning of March 26th the kingdom said it had started a military operation in neighbouring Yemen to push back the Houthis and reinstate the “legitimate government” of President Abd Rabbo Mansour Hadi.

The first air strikes hit Houthi positions in Sana’a, the Yemeni capital, including the airport and the group’s political headquarters. They also targeted military bases controlled by loyalists of Ali Abdullah Saleh, Yemen’s former president, who was ousted in 2011 and has been backing the Houthis, a Shia militia that occupied Sana’a in September and has rapidly taken over swathes of the country.

Adel al-Jubeir, the Saudi ambassador to America, says the strikes are the opening salvo in a campaign involving ten countries—mainly Gulf states as well as Jordan and Egypt. America said it was providing logistical and intelligence support.

The Saudi-led intervention comes after an advance by forces loyal to Houthis and Mr Saleh towards Aden, a strategic southern port to which Mr Hadi had fled earlier this year after the fall of the capital. The Houthi advance worries Saudi Arabia because the militiamen are backed by Iran, its main strategic rival for influence in the region (see article). As the Houthis have moved south, so Iran’s support for them has increased. Tehran recently announced twice-daily flights to Sana’a and said it will supply Yemen with oil.

When the Houthis advanced, taking an important military installation 60km (35 miles) northwest of Aden, Mr Hadi was rumoured to have fled again, this time to Riyadh, the capital of Saudi Arabia. He called for military intervention before he left. Yemenis fear that the Saudi action will catalyse the country’s long-predicted collapse into what Jamal Benomar, the UN envoy to Yemen, has described as an “Iraq-Libya-Syria” scenario.

The air strikes have laid bare the divisions caused by the Houthis’ rise. In the south of the country and in northern tribal areas populated by Sunnis, who fear dominance by the Houthi’s Zaydi sect (a subset of Shia Islam), people are cheering the Saudi-led campaign.

But in Sana’a even the Houthis’ sternest critics are dismayed by the foreign bombardment. Many Yemenis believe it will only lead to more fighting. “Saudi Arabia is fucking our country,” says a Sunni tribesman who spent the night cowering with his family in Sana’a as blasts echoed through the capital.

The anti-Houthi groups’ wish is not to bring back Mr Hadi—a man who ceded control of the capital without a fight six months ago; it is that the Houthi menace be brought to heel.

Yet Saudi Arabia’s attempt to bring this about risks leading to an expansion of sectarian violence between Sunni and Shia. That is because Yemen will inevitably become a proxy battleground for Saudi Arabia, a Sunni bulwark, and Iran, the main Shia power.

Extremist Sunni groups are already active. Yemen is home to al-Qaeda in the Arabian Peninsula (AQAP), al-Qaeda’s deadliest branch, and an affiliate of Islamic State, which claimed responsibility for the suicide bombings of two Zaydi mosques in Sana’a on March 20th, leaving at least 137 people dead.

Before he left the country, Mr Hadi was in the process of forming a 20,000 strong Saudi-backed militia. His opponents accuse him of arming and funding some Sunni extremist groups.

For the Houthis, the Saudi-led operation is a public-relations coup. In a vitriolic and paranoid speech on March 20th, their leader, Abdelmalek al-Houthi, accused the Gulf Arab states and America of plotting to destabilise the country in order to reinstall Mr Hadi as a puppet leader.

The Houthis have evolved into a highly effective guerrilla force after a decade of war against Mr Saleh and Saudi Arabia. With the backing of Saleh loyalists they are likely to prove a tough enemy.

“They control the skies and we control the ground,” says a Houthi man in Sana’a. “This will be just like the sixth war in Saada when the Saudis lost Saudi territory,” he says, referring to an earlier bombing campaign by the kingdom in 2009. Houthis responded to that by crossing the border and humiliating the Saudi army by seizing dozens of towns and villages. On March 26th, after threatening revenge against the “Zionist Saudi regime”, they said that they had fired rockets across the border into Saudi territory. As so often in the Middle East, the Saudis may find that joining a war is easier than winning one.