Index Theorems and Superstring Compactification.
Abstract
This dissertation addresses some issues in the compactification of superstring theories, particularly the lowenergy spectrum of the resulting fourdimensional theory, using techniques which are a generalization of the AtiyahSinger index theorem. Any symmetries of the internal space K become symmetries of the lowenergy lagrangian; continuous symmetries become gauge symmetries and discrete symmetries become global symmetries. The action of these symmetries on the lowenergy fields can be partially determined using charactervalued index theorems. A new derivation of these theorems using the techniques of supersymmetric quantum mechanics is presented here. The first result is that these symmetries act on the lowenergy matter generations in a more general way than would be possible in conventional grand unified models in four dimensions. The particular possibility of familydependent gauge transformations is discussed in some detail, and an example of such a symmetry is given. The second application to the potential appearance of massless E(,6) singlets, with the physical consequence of breaking E(,6) gauge symmetry down to an O(10) or SU(5) subgroup. Mathematically, these massless singlets are related to harmonic vectorbundlevalued differential forms whose ordinary index vanishes. The charactervalued indices do not necessarily vanish, however, and when they do not they signal the presence of these massless singlets.
 Publication:

Ph.D. Thesis
 Pub Date:
 1986
 Bibcode:
 1986PhDT........59G
 Keywords:

 Physics: Elementary Particles and High Energy