Antarctica does not have a capital, for it is not an independent country. Many countries have territorial claims on the continent, but few of them even have cities.
New Zealand, the United Kingdom, France, Norway, Australia, Chile and Argentina all have territorial claims in Antarctica. However, these territories do not have universal recognition among the international community. All territorial claims to the land, in fact, are superseded by the Antarctic Treaty System, a number of treaties that establish Antarctica as a scientific preserve with free movement of scientific teams. The treaties also ban any military activity from taking place on the continent.