Studies on Strings and Anomalies.
Abstract
This thesis involves studies on two different but closely related subjects, namely, strings and anomalies. The string theories offer the hope of unifying all known fundamental interactions. And the only string theories which are consistent, i.e., free of anomalies, are the superstring theories in ten dimensional spacetime with unique internal symmetry groups. After a brief survey of the properties of the various string theories and anomalies, we study in detail the anomalyfree string theories in the compactified dimensions. The general grouptheoretic argument to the dimensional reduction and the definition of the compactification condition of the string theories are given. It is shown by explicit calculations that the E_ 8 times E_ 8 and the SO(16) times SO(16) heterotic string theories, remain anomaly free in every compactified even dimension only if the proper compactification condition is satisfied. Furthermore the global anomaly of the SO(16) times SO(16) heterotic string is derived and possible compactified manifolds are discussed. Finally, we argue that if the GreenSchwarz mechanism makes a theory anomalyfree in 10dimension, then it remains anomalyfree in 8 and 4 dimensions and for the theory to be anomalyfree in 6dimension a consistent constraint on the 10dimensional spin 3/2 fields is needed. The index theorem which is closely related to the anomaly is discussed. We consider the generalized Dirac operator with torsion. It is proved rigorously that the index theorem is independent of torsion. We also calculate the Witten index in superspace. We show that the generalized Witten index in superspace has a close relationship with the superspace SchwingerDewitt heat kernel. Using the generalized Witten index, the superanomaly in YangMills and gravitational backgrounds are evaluated. Furthermore, it is shown how to evaluate effectively the 3dimensional parity anomaly by applying the superspace SchwingerDewitt heat kernel method. Finally, we show that the {rm (4k  1)}dimensional gravity theories in Euclidean space is anomalous.
 Publication:

Ph.D. Thesis
 Pub Date:
 September 1987
 Bibcode:
 1987PhDT........91K
 Keywords:

 Physics: Elementary Particles and High Energy