Kac-Moody algebras and string theory
The focus of this thesis is on (1) the role of Kac-Moody algebras in string theory and the development of techniques for systematically building string theory models based on a higher level (K {>=} 2) KM algebras and (2) fractional superstrings, a new class of solutions based on SU(2){sub K}/U(1) conformal field theories. The content of this thesis is as follows. In chapter two they review KM algebras and their role in string theory. In the next chapter they present two results concerning the construction of modular invariant partition functions for conformal field theories build by tensoring together other conformal field theories. First they show how the possible modular invariants for the tensor product theory are constrained if the allowed modular invariants of the individuals conformal field theory factors have been classified. They illustrate the use of these constraints for theories of the type SU(2){sub K}{sub A} {direct_product} SU(2){sub K}{sub B}, finding all consistent theories for K{sub A} and K{sub B} odd. Second they show how known diagonal modular invariants can be used to construct inherently asymmetric invariants where the holomorphic and anti-holomorphic theories do not share the same chiral algebra. Explicit examples are given. Next, in chapter four they investigate some issues relating to recently proposed fractional superstring theories with D{sub critical} < 10. Using the factorization approach of Gepner and Qiu, they systematically rederive the partition functions of the K = 4, 8, and 16 theories and examine their spacetime supersymmetry. Generalized GSO projection operators for the K = 4 model are found. Uniqueness of the twist field, {phi}{sub K/4}{sup K/4}, as source of spacetime fermions, is demonstrated.
- Research Organization:
- California Institute of Technology (CalTech), Pasadena, CA (United States)
- OSTI ID:
- 39344
- Resource Relation:
- Other Information: TH: Thesis (Ph.D.); PBD: 1993
- Country of Publication:
- United States
- Language:
- English
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