Russian President Vladimir Putin addresses the St. Petersburg International Economic Forum on June 17. (Dmitry Lovetsky/Associated Press)

Max Boot is a senior fellow at the Council on Foreign Relations.

The world is transfixed by Britain’s referendum Thursday over whether to stay in the European Union. Some of the most interested and anxious spectators of the “Brexit” debate are in the Baltic republics, where I recently spent a week meeting with political and military leaders as part of a delegation from the Jamestown Foundation.

Estonia, Latvia and Lithuania know what can happen when Europe isn’t united. Their freedom came to an end in 1940 when Soviet troops marched in, followed by Nazi troops the next year. Britain and France were too busy fighting for their own survival to offer assistance. The United States was still pursuing isolationism. Nor was the West able to do anything when, in 1944, the Red Army reoccupied the Baltics, imposing a brutal dictatorship that would last until 1991.

The Balts are prosperous and free now, but for how long? With a total population of just 6.2 million and just 56,000 military troops, the Baltic states sit next door to Russia, with 142 million people and more than 3 million troops in its active duty and reserve forces. Already Russia’s dictator, Vladimir Putin, has invaded Georgia and Ukraine. What is to stop him from marching into the Baltics?

The immediate deterrent is provided by NATO: All of the Baltic states are NATO members, and other NATO members, including the United States, are pledged to come to their defense if they are attacked. But the Balts are also members of the European Union, and they are convinced that a strong and vibrant E.U. is also necessary to maintain their prosperity and security. The E.U. enforces economic sanctions on Russia and provides the financial support needed for its more vulnerable members in Eastern Europe to withstand Russia’s economic pressure, such as threats to shut off the flow of natural gas.

That is why the Balts are alarmed at the prospect of Brexit passing. Their message for Britons is: “Lead, not leave.”

The Balts admire the Brits and believe that with their shared devotion to free trade, British membership in the E.U. serves their interests, because it counterbalances the more statist and protectionist impulses of Germany and France. Britain is also in favor of a stronger anti-Russian stance than are Germany and France.

If Britain left the E.U., the Balts fear that Scotland, which is more pro-E.U. than the rest of the United Kingdom, would leave Britain. Scotland just happens to be where Britain’s nuclear deterrent is based aboard four Vanguard-class submarines. The naval base at Faslane could be relocated, but it would be costly to do so at a time when the British defense budget has already been cut to the bone. Odds are that a Britain outside the E.U. would be smaller and weaker than it is today.

Moreover, if Britain does vote for Brexit, it will lead to a period of turmoil with Brits and other Europeans debating the nature of their future relationship. Britain and the E.U. will have to pass a trade treaty, and the terms are sure to be contentious. While the negotiations are going on, Europeans will be focused inward — not at the external threat to the east.

The Balts fear, finally, that a British exit could set off a chain reaction of other exits. There is great unhappiness with the E.U. in many member states, and Putin has been supporting anti-E.U. parties in Europe of both the far left and far right.

Nigel Farage, leader of the UK Independence Party and a leading pro-Brexit voice, has harsh words for Brussels but nothing but kind words for Moscow. He has expressed admiration for Putin and been a regular guest on the Russia Today propaganda channel.

Campaigning resumes ahead of Britain's referendum on European Union membership after the killing of Labour MP Jo Cox. (Reuters)

France’s far-right National Front, led by Marine Le Pen, has admitted receiving tens of millions of euros in “loans” from a Kremlin-linked bank. Russia is also supporting in various ways other extremist parties, including the far-right Jobbik in Hungary, the far-left Podemos in Spain, the far-left Syriza in Greece and the far-right Freedom Party in Austria, that are pro-Russia and anti-E.U. Oh, and Putin goes out of his way to praise Donald Trump, who has called NATO “obsolete” and vowed to improve relations with Russia.

It’s clear that the Russians are hoping to promote disunity in the West by breaking up the two alliances that oppose them — NATO and the E.U. The Balts are concerned — and so should we be — that a British vote for Brexit would play into Putin’s hands. The last thing the West needs is to see Europe divided, allowing Putin’s Russia to use a divide-and-conquer strategy. British voters may not care what anyone else thinks, but there’s a good reason their allies want them to stay in the E.U.