Kac-Moody Symmetries of Kaluza-Klein Theories

The authors identify symmetries of the four-dimensional Lagrangian, including the massive states, obtained via Kaluza-Klein compactification from gravity in five dimensions and ground state M⁴×S¹. The symmetries are described by (1) a Kac-Moody extension of the Poincar\'e algebra, (2) a Virasoro algebra of internal symmetries including the Salam-Strathdee SO(1,2), and (3) a mixing of (1) and (2). All symmetries are spontaneously broken save for Poincar\'e {} U(1). The Goldstone bosons provide masses for the spin-2 tower. Higher dimensions and supergravity are discussed.