Kac-Moody algebras and string theory

Citation

Cleaver, Gerald B. (1993) Kac-Moody algebras and string theory. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/FXSK-JK33. https://resolver.caltech.edu/CaltechETD:etd-03062009-160921

Abstract

NOTE: Text or symbols not renderable in plain ASCII are indicated by [...]. Abstract is included in .pdf document. 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 higher level K ≥ 2) KM algebras and (2) fractional superstrings, a new class of solutions based on SU(2)[subscript K]/U(1) conformal field theories. The content of this thesis is as follows. In chapter two we review KM algebras and their role in string theory. In the next chapter, we present two results concerning the construction of modular invariant partition functions for conformal field theories built by tensoring together other conformal field theories. This is based upon our research in ref. [2]. First we show how the possible modular invariants for the tensor product theory are constrained if the allowed modular invariants of the individual conformal field theory factors have been classified. We illustrate the use of these constraints for theories of the type [...], finding all consistent theories for K[subscript A] and K[subscript B] odd. Second we 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 we investigate some issues relating to recently proposed fractional superstring theories with D[subscript critical] < 10. Using the factorization approach of Gepner and Qiu, we 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, [...] as source of spacetime fermions, is demonstrated. Our research was originally presented in refs. [3, 4]

Thesis Files