Calabi-Yau compactifications and the global structure of the standard group

Abstract

The "standard group" of elementary particle theory is locally isomorphic to SU(3) ×SU(2)×U(1). The global structure is completely fixed in unified theories, often in a subtle way; and such theories can be physically unacceptable if they predict the "wrong" global structure for the standard group. A particularly striking example of this is provided by Calabi-Yau compactifications of string theory with the linear (rather than the more conventional spinor) connection interpreted as an E8 connection. Remarkably, these more unconventional compactifications break E8 to a group which is locally isomorphic to the standard group (instead of E6); but they are physically unacceptable, and we argue that the basic reason for this is their failure to produce the correct global structure. © 1996 American Institute of Physics.