I. The No-Drama School of Zombie Realpolitik
There are many varieties of realism, but all realists start with a common assumption: that anarchy is the overarching constraint of world politics. Anarchy does not necessarily mean chaos or disorder, but rather the absence of a centralized, legitimate authority.
No matter what ardent cosmopolitans or crazed conspiracy theorists believe, there is no world government. With no monopoly on the use of force in world politics, actors must take their own "self-help" measures to ensure their continued existence.
In a world of anarchy, the only currency that matters is power -- the material capability to ward off pressure or coercion, while being able to influence others. The anarchic global structure also makes it impossible for governments to fully trust each other, forcing states to be guided solely by their own national interests.
As this summary might suggest, realism has a rather dystopian and jaundiced view of the world. In other words, it is perfectly comfortable in the zombie universe -- particularly the world of George Romero's films.
How would the introduction of flesh-eating ghouls affect world politics? The realist answer is simple if surprising: International relations would be largely unaffected. Although some would see in a zombie invasion a new existential threat to the human condition, realists would be unimpressed by the claim that the zombies' arrival would lead to any radical change in human behavior. To them, a plague of the undead would merely echo older plagues, from the Black Death of the 14th century to the 1918 influenza pandemic. To paraphrase Thucydides, the realpolitik of zombies is that the strong will do what they can and the weak must suffer devouring by reanimated, ravenous corpses.
Realists also predict balance-of-power politics, so wouldn't the specter of the undead create a balancing coalition of humans against ghouls? This possibility cannot be ruled out. If zombies emerged from central Eurasia, for example, their capacity to spread quickly could trigger an alliance designed to prevent zombie hordes from taking over the continent. However, buck-passing would be an equally likely outcome. In a buck-passing situation, states would refrain from taking an active stance against the zombies in the hopes that other countries would do the dirty work of uniting to slay the demon hordes.
States could also exploit the threat from the living dead to acquire new territory, squelch irredentist movements, settle old scores, or subdue enduring rivals. The People's Republic of China could use the zombie threat to justify an occupation of Taiwan. Russia could use the same excuse to justify intervention in its near abroad. The United States would not be immune from the temptation to exploit the zombie threat as a strategic opportunity. How large would the army of the Cuban undead need to be to justify the deployment of the 82nd Airborne?
But in the end, realists, particularly American realists, would no doubt evoke the cautionary words of U.S. President John Quincy Adams and warn against going abroad "in search of monsters to destroy."